API marketplace

Uniform circular-motion physics as an API, computed locally and deterministically. The centripetal-force endpoint computes the centripetal acceleration a = v²/r = ω²·r — always pointing toward the centre — and the centripetal force F = m·a that holds a body on its circular path, from the mass, the radius and either the linear or the angular velocity, and reports the equivalent g-force. The angular endpoint converts between every way of describing rotation — angular velocity (rad/s), revolutions per minute, frequency, period and, given a radius, the linear (tangential) velocity — using ω = 2π·f = 2π/T = v/r. The centrifuge endpoint computes the relative centrifugal force (RCF, in g) of a centrifuge rotor from its speed in rpm and radius, RCF = ω²·r / g, or inverts it to give the rpm needed to reach a target RCF. Masses are in kg, radii in m (mm for the centrifuge), velocities in m/s, angular velocities in rad/s and forces in N. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, mechanical, automotive, lab-centrifuge and amusement-ride app developers, rotational-motion and g-force tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is uniform circular motion; for gravitational orbits use a gravitation API, for a vehicle on a banked curve a banked-curve API and for pendulum oscillation a pendulum API.

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100.0%

Latency

167ms

Subs

3,462

NTC-thermistor sensor maths as an API, computed locally and deterministically. The steinhart-hart endpoint converts between resistance and temperature using the Steinhart-Hart equation, 1/T = A + B·ln R + C·(ln R)³ — the most accurate NTC model — in both directions, solving the resistance at a given temperature with Cardano's cubic formula. The beta endpoint uses the simpler two-point Beta model, 1/T = 1/T0 + (1/β)·ln(R/R0) and R = R0·exp(β·(1/T − 1/T0)), to convert resistance to temperature or back from a reference resistance R0 at T0 (default 25 °C) and the beta coefficient. The divider endpoint recovers the thermistor's resistance from a voltage-divider reading — low-side R = Rs·Vout/(Vsupply − Vout) or high-side — so an ADC voltage can be turned into a resistance and then a temperature. Resistance is in ohms, temperature in °C (kelvin also returned), voltages in volts and beta in kelvin. Everything is computed locally and deterministically, so it is instant and private. Ideal for embedded, IoT, HVAC-control, 3D-printer and battery-management app developers, temperature-sensing and calibration tools, and electronics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is NTC thermistor conversion; for a generic resistive divider use an LED-resistor or voltage-drop API and for thermal expansion a thermal-expansion API.

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100.0%

Latency

161ms

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4,467

Chemical reaction-stoichiometry maths as an API, computed locally and deterministically. The limiting-reagent endpoint takes two reactants with their amounts in moles and their balanced-equation coefficients and finds which one runs out first — the limiting reagent — by comparing the moles/coefficient ratio (the reaction extent), and returns how much of the excess reagent is left over. The yield endpoint computes the theoretical yield of a product, in moles and grams, from the limiting reagent and the product's stoichiometric coefficient and molar mass, n_product = n_limiting·(coeff_product/coeff_limiting), and — given the actual yield — the percent yield. The mole-mass endpoint converts between moles, mass and the number of particles for a given molar mass, using moles = mass / molar_mass and N = moles · Avogadro's number (6.02214076e23). Amounts are in moles, masses in grams and molar masses in g/mol. Everything is computed locally and deterministically, so it is instant and private. Ideal for chemistry-education, lab, pharmaceutical and chemical-engineering app developers, reaction-planning and yield tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is reaction stoichiometry; for a compound's molar mass from its formula use a molar-mass API and for solution concentrations a dilution API.

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100.0%

Latency

184ms

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4,333

Electrochemistry maths as an API, computed locally and deterministically. The nernst endpoint applies the Nernst equation, E = E° − (R·T/nF)·ln Q, to give the actual electrode or cell potential under non-standard conditions from the standard potential E°, the number of electrons transferred n, the reaction quotient Q and the temperature — at 25 °C this reduces to E = E° − (0.05916/n)·log10 Q, and a larger Q (more product) lowers the potential. The cell-potential endpoint computes a galvanic cell's standard EMF from the cathode and anode standard reduction potentials, E°cell = E°cathode − E°anode, together with the standard Gibbs free energy ΔG° = −nF·E°cell and whether the reaction is spontaneous. The equilibrium endpoint computes the equilibrium constant of a redox reaction, K = exp(nF·E°cell / RT), and the corresponding ΔG°, from the standard cell potential and the electrons transferred. Potentials are in volts, energies in kJ/mol, the Faraday constant is 96485 C/mol and the gas constant 8.314 J/mol·K. Everything is computed locally and deterministically, so it is instant and private. Ideal for chemistry-education, battery, corrosion, electroplating and electroanalytical app developers, galvanic-cell and redox tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is electrochemistry; for acid-base pH use a pH API and for reaction-rate kinetics an Arrhenius API.

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100.0%

Latency

156ms

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4,664

Moist-air (psychrometric) thermodynamics as an API, computed locally and deterministically. The dewpoint endpoint computes the dew-point temperature and the saturation and actual water-vapour pressures from a dry-bulb temperature and relative humidity, using the Magnus-Tetens relation over water, es = 6.112·exp(17.62·T/(243.12+T)) hPa — the dew point is the temperature to which air must cool for water vapour to start condensing. The humidity-ratio endpoint computes the humidity ratio (mixing ratio) W = 0.621945·Pw/(P−Pw), the specific and absolute humidity, the vapour pressure and the moist-air enthalpy h = 1.006·T + W·(2501 + 1.86·T) kJ per kg of dry air, at any total pressure (default sea-level 101325 Pa). The wet-bulb endpoint computes the wet-bulb temperature with the Stull (2011) empirical fit and the wet-bulb depression, the gap between dry- and wet-bulb that widens as the air gets drier. Temperatures are in °C, relative humidity in %, pressures in Pa. Everything is computed locally and deterministically, so it is instant and private. Ideal for HVAC, building-physics, meteorology, drying, greenhouse and data-centre-cooling app developers, comfort and condensation-risk tools, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is moist-air psychrometrics; for ASHRAE ventilation airflow use a ventilation API, for the WBGT heat-stress index a WBGT API and for the standard atmosphere an atmosphere API.

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100.0%

Latency

158ms

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4,556

Surface-tension and small-scale fluid-physics maths as an API, computed locally and deterministically. The capillary-rise endpoint applies Jurin's law, h = 2γ·cosθ / (ρ·g·r), to give the height a liquid climbs (or, for a contact angle above 90° like mercury, is depressed) in a narrow tube from its surface tension, the tube radius, the liquid density and the contact angle — and can solve the surface tension back from a measured rise. The laplace-pressure endpoint computes the Young-Laplace excess pressure across a curved interface: a liquid droplet ΔP = 2γ/r, a soap bubble ΔP = 4γ/r (two surfaces) and a cylindrical jet ΔP = γ/r. The poiseuille endpoint applies the Hagen-Poiseuille law, Q = π·r⁴·ΔP / (8·μ·L), for laminar flow in a pipe, returning the volumetric flow rate, the average velocity and the peak centreline velocity (twice the average) from the radius, the pressure drop, the fluid viscosity and the length. Surface tension is in N/m, lengths in m, density in kg/m³, viscosity in Pa·s and pressures in Pa; water is γ ≈ 0.0728 N/m at 20 °C. Everything is computed locally and deterministically, so it is instant and private. Ideal for microfluidics, fluid-engineering, lab-on-a-chip, inkjet and coating app developers, capillary-action and wicking tools, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is surface tension and capillarity; for incompressible Bernoulli flow use a Bernoulli API and for pipe friction a Darcy API.

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163ms

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3,409

Nuclear-physics maths as an API, computed locally and deterministically. The binding-energy endpoint computes a nucleus's mass defect, Δm = Z·m_H + N·m_n − M_atom, and its binding energy E = Δm·c² (1 u = 931.494 MeV) and binding energy per nucleon, from the proton and neutron counts and the measured atomic mass. The semf endpoint estimates the binding energy from the semi-empirical (Bethe-Weizsäcker) mass formula, breaking it into the volume, surface, Coulomb, asymmetry and pairing terms, from just the mass number and proton number. The q-value endpoint computes the energy released or absorbed in a nuclear reaction from the masses of the reactants and products, Q = (Σm_reactants − Σm_products)·c², classifying it as exothermic (fusion of light nuclei or fission of heavy ones) or endothermic. Masses are in atomic mass units and energies in MeV and joules. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, nuclear-engineering, astrophysics and science app developers, reactor and reaction tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is nuclear binding and reactions; for radioactive decay use a half-life API and for atomic energy levels a quantum API.

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Latency

164ms

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3,407

Quantum and atomic-physics maths as an API, computed locally and deterministically. The photoelectric endpoint applies Einstein's photoelectric equation, KE = hf − φ — from the incident light's wavelength or frequency and a metal's work function it gives the photon energy, whether electrons are emitted, their maximum kinetic energy, the threshold frequency and wavelength (f₀ = φ/h), the maximum electron speed and the stopping voltage. The bohr endpoint computes the Bohr-model energy level Eₙ = −13.606·Z²/n² eV and orbital radius rₙ = 0.529·n²/Z Å of a hydrogen-like atom, the ionisation energy, and — given a second level — the wavelength of the emitted or absorbed photon. The rydberg endpoint computes a spectral line's wavelength from the Rydberg formula, 1/λ = R·Z²·(1/n₁² − 1/n₂²), and names its series (Lyman, Balmer, Paschen …) and spectral region. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, spectroscopy, astronomy and science app developers, atomic-physics and spectral tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is quantum and atomic physics; for electromagnetic wavelength and photon energy use a wavelength API and for special relativity a relativity API.

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100.0%

Latency

158ms

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Betting-odds maths as an API, computed locally and deterministically. The convert endpoint translates a price between every format used by bookmakers — decimal (European), fractional (UK), American (moneyline) and the implied probability — give it any one and it returns all the others, with the implied probability that the odds represent (1 ÷ decimal). The payout endpoint computes the profit and total return for a stake at given decimal or American odds. The parlay endpoint combines several decimal-odds selections into one accumulator by multiplying them, returning the combined odds, the implied probability and the payout for a stake — every leg must win, so the payout grows fast while the probability shrinks. Decimal odds are the total return per unit staked, American odds are at least +100 for an underdog or −100 or lower for a favourite, and fractional odds look like 5/2. Everything is computed locally and deterministically, so it is instant and private. Ideal for sports-betting, fantasy, odds-comparison and gaming app developers, bet-slip and value tools, and probability education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is odds conversion; for probability distributions use a probability API.

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Latency

174ms

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4,545

Isentropic compressible-flow (gas-dynamics) maths as an API, computed locally and deterministically. The isentropic endpoint gives the stagnation-to-static ratios of a perfect gas from a Mach number and the heat-capacity ratio γ (1.4 for air): the temperature ratio T0/T = 1 + (γ−1)/2·M², the pressure ratio p0/p = (T0/T)^(γ/(γ−1)), the density ratio and the area ratio A/A* relative to the sonic throat, and classifies the flow as subsonic, sonic or supersonic. The stagnation endpoint turns a static temperature and pressure plus a Mach number into the stagnation (total) conditions, the speed of sound a = √(γRT) and the flow velocity. The mach endpoint inverts the relations, solving the Mach number from a pressure, temperature or area ratio — an area ratio gives both the subsonic and supersonic roots — or from a velocity and temperature. Everything is computed locally and deterministically, so it is instant and private. Ideal for aerospace, propulsion, nozzle-design and wind-tunnel app developers, supersonic-flow and ducting tools, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is compressible isentropic flow; for the standard atmosphere use an atmosphere API and for incompressible Bernoulli flow a Bernoulli API.

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100.0%

Latency

177ms

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3,826

Capacitor maths as an API, computed locally and deterministically. The energy endpoint computes the stored energy and charge of a capacitor from any two of the capacitance, the voltage and the charge — E = ½CV² = ½QV and Q = CV — in joules, millijoules and coulombs. The charging endpoint models the RC charging and discharging transient: the time constant τ = RC, the voltage at a given time, V(t) = Vs(1 − e^(−t/RC)) when charging or V(t) = V₀·e^(−t/RC) when discharging, and the percent charged, or — given a target voltage — the time to reach it; a capacitor reaches about 63 % of the way in one time constant and over 99 % in five. The combination endpoint computes the total capacitance of capacitors in series (1/C = Σ1/Cᵢ) or parallel (C = ΣCᵢ). Capacitance accepts farads or the handy µF/nF/pF units. Everything is computed locally and deterministically, so it is instant and private. Ideal for electronics, maker, embedded and circuit-design app developers, power-supply and timing tools, and electronics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is capacitor maths; for AC reactance and resonance use a resonance API and for LED resistor sizing an LED-resistor API.

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100.0%

Latency

153ms

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3,975

Fixed-income bond maths as an API, computed locally and deterministically. The price endpoint computes a bond's price from its face value, coupon rate, yield to maturity, years to maturity and coupon frequency — Price = Σ coupon/(1+y)ᵗ + face/(1+y)ⁿ with y the periodic yield — and reports the clean price as a percent of par, the annual coupon, the current yield and whether the bond trades at a premium, discount or par. The yield endpoint inverts this, solving for the yield to maturity that matches a given market price by bisection, with the current yield. The duration endpoint computes the Macaulay duration (the cash-flow-weighted average time), the modified duration (which approximates the percent price change per 1 % yield move), the convexity and the DV01 (the price change per basis point). A zero-coupon bond is just coupon rate 0. Everything is computed locally and deterministically, so it is instant and private. Ideal for fintech, fixed-income, treasury and portfolio app developers, bond-analytics and risk tools, and finance education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is bond analytics; for option pricing use an options API and for NPV and IRR an NPV API.

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100.0%

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201ms

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Black-Scholes option-pricing maths as an API, computed locally and deterministically. The black-scholes endpoint prices European call and put options from the spot price, strike, time to expiry, risk-free rate, volatility and an optional dividend yield — Call = S·e^(−qT)·Φ(d1) − K·e^(−rT)·Φ(d2) — returning both prices, the intermediate d1 and d2, and the put-call parity figure. The greeks endpoint computes the full set of option sensitivities for the call and the put: delta, gamma, theta (per year and per day), vega and rho, the quantities traders use to hedge and manage risk. The implied-volatility endpoint inverts the model, solving by bisection for the volatility that reproduces a given option market price. Rates, volatilities and dividend yields are decimals (0.05 = 5 %) and time to expiry is in years. Everything is computed locally and deterministically, so it is instant and private. Ideal for fintech, trading, quantitative-finance and derivatives app developers, options analytics and risk tools, and finance education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is options pricing; for NPV and IRR use an NPV API and for CAGR and real returns an investment API.

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194ms

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Geotechnical foundation maths as an API, computed locally and deterministically. The factors endpoint computes the Terzaghi/Vesic bearing-capacity factors Nc, Nq and Nγ from a soil friction angle — Nq = e^(π·tanφ)·tan²(45+φ/2), Nc = (Nq−1)·cotφ and Nγ = 2(Nq+1)·tanφ. The bearing-capacity endpoint computes the ultimate, net and allowable bearing capacity of a strip, square or circular footing from the cohesion, friction angle, soil unit weight, footing width and founding depth, qu = sc·c·Nc + γ·D·Nq + sγ·γ·B·Nγ, breaking it into its cohesion, surcharge and self-weight components and dividing by a factor of safety (default 3) for the allowable value. The settlement endpoint computes the immediate elastic settlement of a footing, s = q·B·(1−ν²)·I / E, from the applied pressure, the footing width, the soil elastic modulus and Poisson's ratio. Cohesion and pressures are in kilopascals, unit weight in kN/m³ and lengths in metres. Everything is computed locally and deterministically, so it is instant and private. Ideal for civil-engineering, geotechnical, foundation-design and construction app developers, footing-sizing and feasibility tools, and engineering education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is foundation bearing capacity; for lateral earth pressure on walls use an earth-pressure API and for open-channel flow a Manning API.

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Latency

167ms

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3,266

Printed-circuit-board design maths as an API, computed locally and deterministically. The trace-width endpoint applies the IPC-2221 standard to find the minimum copper trace width for a current and an allowable temperature rise, A = (I/(k·ΔT^0.44))^(1/0.725) with k = 0.048 for outer layers and 0.024 for inner, returning the cross-section and the width in mils and millimetres for a given copper weight. The trace-resistance endpoint computes a trace's resistance from its width, length and copper thickness, R = ρ·L/(W·t), with the copper temperature coefficient, and — given a current — the voltage drop and power dissipation. The microstrip endpoint computes the characteristic impedance of a microstrip line by the Hammerstad model from the trace width, the dielectric height and the dielectric constant (about 4.5 for FR4), with the effective permittivity and propagation delay for controlled-impedance routing. Everything is computed locally and deterministically, so it is instant and private. Ideal for electronics, hardware, embedded and PCB-design app developers, board-layout and signal-integrity tools, and electronics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is PCB design; for resistor colour codes use a resistor API and for general Ohm's-law maths an Ohm's-law API.

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157ms

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3,174

Homebrewing maths as an API, computed locally and deterministically. The abv endpoint computes the alcohol by volume from the original and final gravity — both the simple (OG − FG)·131.25 estimate and a more accurate high-gravity formula — along with the apparent and real attenuation and the calories per 12 oz serving. The gravity endpoint converts freely between specific gravity, degrees Plato and Brix (the three ways brewers and winemakers measure dissolved sugar) and reports the gravity points. The ibu endpoint computes hop bitterness in International Bitterness Units by the Tinseth formula from the hop alpha-acid percentage, the weight, the boil time, the batch volume and the wort gravity, returning the utilization and the alpha-acid concentration too. Gravities are specific gravity such as 1.050, hop weight in grams, boil time in minutes and volume in litres. Everything is computed locally and deterministically, so it is instant and private. Ideal for homebrew, craft-beer, cidery and winemaking app developers, recipe and batch tools, and brewing education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is brewing maths; for a brewery directory use a beer API and for coffee brew ratios a coffee API.

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179ms

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4,215

Population-genetics maths as an API, computed locally and deterministically. The hardy-weinberg endpoint applies the Hardy-Weinberg principle, p² + 2pq + q² = 1 — give a dominant allele frequency p, a recessive q, or the homozygous-recessive (affected) frequency q² and it returns all the allele and genotype frequencies, including the carrier frequency 2pq. The punnett endpoint crosses two parent genotypes and returns the offspring genotype and phenotype ratios, handling a single gene (a monohybrid 1:2:1 / 3:1 cross), two genes (a dihybrid 9:3:3:1 cross) and up to four genes by independent assortment. The carrier endpoint takes the incidence of a recessive disease — as a fraction or one-in-N — and returns the recessive allele frequency q = √incidence, the carrier frequency 2pq, the one-in-N carrier rate and, for a given population, the expected number of carriers and affected individuals. Everything is computed locally and deterministically, so it is instant and private. Ideal for genetics-education, genetic-counselling, breeding and biology app developers, inheritance and risk tools, and biology teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is population genetics; for DNA sequence analysis use a DNA API.

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173ms

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Classifier-evaluation maths as an API, computed locally and deterministically. The confusion endpoint turns the four cells of a binary confusion matrix — true and false positives and negatives — into the full metric suite: accuracy, precision, recall (sensitivity), specificity, the F1 score, the Matthews correlation coefficient (robust to class imbalance), balanced accuracy, negative predictive value, the false-positive and false-negative rates and the prevalence. The diagnostic endpoint applies Bayes' theorem to a medical or screening test: from its sensitivity, specificity and the prevalence (pre-test probability) it gives the positive and negative predictive values, the positive and negative likelihood ratios and the diagnostic odds ratio. The fbeta endpoint computes the Fβ score from precision and recall (or from the raw counts) for any β — β = 1 is F1, larger β weights recall, smaller β weights precision. Metrics whose denominator is zero are returned as null rather than erroring. Everything is computed locally and deterministically, so it is instant and private. Ideal for machine-learning, data-science, medical-testing and analytics app developers, model-evaluation and screening tools, and statistics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is classifier evaluation; for descriptive statistics and regression use a statistics API and for hypothesis tests an inference API.

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141ms

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DNA/RNA sequence-analysis maths as an API, computed locally and deterministically. The analyze endpoint reports the length and base composition of a sequence, the GC and AT content, the complement, the reverse and the reverse complement (the opposite strand read 5'→3'), and the approximate single-stranded molecular weight. The translate endpoint transcribes DNA to mRNA (T→U) and translates it to protein with the standard genetic code in reading frame 1, 2 or 3, giving the one-letter amino-acid sequence, the protein length and the number of stop codons. The melting endpoint estimates a primer's melting temperature with the Wallace rule, 4·(G+C) + 2·(A+T), for short oligos and a salt-adjusted basic formula for longer ones. Sequences are case- and whitespace-insensitive and accept A, C, G, T for DNA or U for RNA. Everything is computed locally and deterministically, so it is instant and private. Ideal for bioinformatics, molecular-biology, genomics and lab app developers, primer-design and sequence-inspection tools, and biology education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is sequence analysis; for genome assembly data use a genomes API.

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157ms

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Internal-combustion engine maths as an API, computed locally and deterministically. The displacement endpoint computes an engine's swept volume from the bore, the stroke and the number of cylinders, V = (π/4)·bore²·stroke per cylinder, in cubic centimetres, litres and cubic inches, and classifies the bore-to-stroke geometry as oversquare, square or undersquare. The compression endpoint relates the compression ratio and the clearance volume, CR = (swept + clearance)/clearance — give the clearance to get the ratio or the ratio to get the clearance — and, with a boost pressure, estimates the effective compression ratio of a forced-induction engine. The power-to-weight endpoint computes the power-to-weight ratio in horsepower per tonne, kilowatts per tonne and watts per kilogram, the weight per horsepower, and, with a displacement, the specific output in horsepower per litre. Bore and stroke are in millimetres, volumes in cc, weight in kilograms and power in horsepower or kilowatts. Everything is computed locally and deterministically, so it is instant and private. Ideal for automotive, motorsport, motorcycle and engine-builder app developers, build-spec and tuning tools, and mechanical education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is engine geometry and tuning; for EPA fuel-economy data use a fuel-economy API and for tyre sizes a tyre-calculator API.

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191ms

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Gaussian-beam laser-optics maths as an API, computed locally and deterministically. The beam endpoint propagates a Gaussian beam from its wavelength and waist radius: the Rayleigh range z_R = π·w₀²/λ and depth of focus, the divergence half- and full-angle θ = λ/(π·w₀), and — for a given distance — the beam radius and diameter w(z) = w₀·√(1+(z/z_R)²); an optional M² beam-quality factor scales it for real beams. The focus endpoint computes the diffraction-limited focused spot of a lens, w_f = λ·f/(π·w_in), with the depth of focus and the f-number, so you can size the spot a lens will deliver. The irradiance endpoint turns a beam power and spot size into the beam area and the average and on-axis peak irradiance (power density) in W/m² and W/cm². Wavelengths are in nanometres, sizes in millimetres or micrometres, distances in metres and power in watts. Everything is computed locally and deterministically, so it is instant and private. Ideal for photonics, laser-engineering, materials-processing and optics app developers, beam-delivery and laser-safety tools, and physics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is Gaussian-beam laser optics; for refraction use a Snell API and for thin-lens imaging a lens API.

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182ms

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Modular-arithmetic maths as an API, computed locally and deterministically with exact big-integer arithmetic. The power endpoint computes modular exponentiation, aᵇ mod m, by square-and-multiply, fast and exact even for the huge exponents used in cryptography. The inverse endpoint finds the modular multiplicative inverse a⁻¹ mod m with the extended Euclidean algorithm, returning the inverse when a and m are coprime and reporting the gcd when no inverse exists. The totient endpoint computes Euler's totient φ(n) — the count of integers from 1 to n coprime to n — with the prime factorization it comes from, and an optional Euler-theorem check that a^φ(n) ≡ 1 (mod n) for a coprime base. These are the building blocks of RSA and much of modern cryptography. Inputs are integers and can be passed as strings for very large values. Everything is computed locally and deterministically, so it is instant and private. Ideal for cryptography, security, blockchain and mathematics app developers, RSA and number-theory tools, and computer-science education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is modular arithmetic; for prime factorization and GCD use a number-theory API and for integer sequences a sequences API.

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166ms

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Discounted-cash-flow investment-appraisal maths as an API, computed locally and deterministically. The npv endpoint computes the net present value of a project from an upfront outlay, a series of future net cash flows and a discount rate, NPV = −initial + Σ CFₜ/(1+r)ᵗ, and reports the present value of the inflows, the profitability index and a plain accept-or-reject decision. The irr endpoint solves the internal rate of return — the discount rate that makes the NPV zero — by robust bisection over the cash flows, the figure you compare against a hurdle rate. The payback endpoint computes both the simple payback period, when the cumulative cash flow first recovers the outlay, and the discounted payback period, which discounts each flow first. Cash flows are passed as a comma-separated list, one per period. Everything is computed locally and deterministically, so it is instant and private. Ideal for finance, corporate, fintech and project-management app developers, capital-budgeting and feasibility tools, and finance education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is capital budgeting; for loan amortization use a loan API and for CAGR and real returns an investment API.

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171ms

Subs

3,033

Gas-mixture maths as an API, computed locally and deterministically. The partial-pressure endpoint applies Dalton's law — give a list of component partial pressures and it sums them to the total and returns each gas's mole fraction; or give a total pressure and a mole fraction to get a partial pressure; or component and total moles to get a mole fraction (and a partial pressure when a total pressure is supplied). The mole-fraction endpoint takes the moles of each component and returns every mole fraction and, with a total pressure, the partial pressures; supply the molar masses too and it adds the mass fractions and the average molar mass of the mixture. The effusion endpoint applies Graham's law, rate₁/rate₂ = √(M₂/M₁), to compare how fast two gases effuse or diffuse from their molar masses, naming the faster gas and the time ratio. Everything is computed locally and deterministically, so it is instant and private. Ideal for chemistry-education, laboratory, process and scuba app developers, gas-blending and stoichiometry tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is gas-mixture maths; for the ideal-gas law of a single gas use a gas-law API and for molar mass from a formula a molar-mass API.

Uptime

100.0%

Latency

170ms

Subs

3,830