{"openapi":"3.1.0","info":{"title":"Waveguide API","version":"1.0.0","description":"Rectangular-waveguide microwave maths as an API, computed locally and deterministically. The cutoff endpoint computes the cutoff frequency fc = (c/2)·√((m/a)²+(n/b)²) and cutoff wavelength of any TEmn or TMmn mode of a rectangular waveguide of inner width a and height b — below the cutoff a mode is evanescent and cannot propagate, and for the usual a > b the dominant mode is TE10 with fc = c/(2a). The guide-wavelength endpoint computes, at an operating frequency, the free-space wavelength, the guide wavelength λg = λ0/√(1−(fc/f)²) which is longer than free space, and the phase velocity (greater than c) and group velocity (the energy speed, below c). The modes endpoint lists every mode that propagates at a given frequency, sorted by cutoff, and identifies the dominant mode — so single-mode operation needs the frequency between the first and second cutoffs. Dimensions are in millimetres and frequencies in gigahertz, with c = 299,792,458 m/s. Everything is computed locally and deterministically, so it is instant and private. Ideal for RF, microwave, radar, satellite and antenna-feed app developers, waveguide-band and component-design tools, and electromagnetics education. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is metallic rectangular waveguide; for optical-fibre guiding use a fibre API and for SWR a VSWR API.","contact":{"name":"PremiumApi","url":"https://www.oanor.com/by/premiumapi"}},"servers":[{"url":"https://api.oanor.com/waveguide-api","description":"oanor gateway"}],"tags":[{"name":"Waveguide"},{"name":"Meta"}],"components":{"securitySchemes":{"oanorKey":{"type":"apiKey","in":"header","name":"x-oanor-key","description":"Get your key at https://www.oanor.com/developer/keys"}}},"security":[{"oanorKey":[]}],"paths":{"/v1/cutoff":{"get":{"operationId":"get_v1_cutoff","tags":["Waveguide"],"summary":"Cutoff frequency","description":"","parameters":[{"name":"width","in":"query","required":true,"description":"Inner width a (mm)","schema":{"type":"string"},"example":"22.86"},{"name":"height","in":"query","required":true,"description":"Inner height b (mm)","schema":{"type":"string"},"example":"10.16"},{"name":"m","in":"query","required":false,"description":"Mode index m","schema":{"type":"string"},"example":"1"},{"name":"n","in":"query","required":false,"description":"Mode index n","schema":{"type":"string"},"example":"0"},{"name":"mode_type","in":"query","required":false,"description":"TE or TM","schema":{"type":"string"},"example":"TE"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"mode":"TE10","note":"Cutoff frequency fc = (c/2)·√((m/a)²+(n/b)²). Below fc the mode is evanescent (cannot propagate). For the usual a > b, the dominant mode is TE10 with fc = c/(2a).","inputs":{"m":1,"n":0,"width_mm":22.86,"height_mm":10.16,"mode_type":"TE"},"cutoff_frequency_ghz":6.55714,"cutoff_wavelength_mm":45.72},"meta":{"timestamp":"2026-06-05T11:30:30.205Z","request_id":"70a99c7f-718e-4159-a4e7-e83cac769e42"},"status":"ok","message":"Cutoff frequency","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/guide-wavelength":{"get":{"operationId":"get_v1_guide_wavelength","tags":["Waveguide"],"summary":"Guide wavelength","description":"","parameters":[{"name":"width","in":"query","required":true,"description":"Inner width a (mm)","schema":{"type":"string"},"example":"22.86"},{"name":"height","in":"query","required":true,"description":"Inner height b (mm)","schema":{"type":"string"},"example":"10.16"},{"name":"frequency","in":"query","required":true,"description":"Frequency (GHz)","schema":{"type":"string"},"example":"10"},{"name":"m","in":"query","required":false,"description":"Mode index m","schema":{"type":"string"},"example":"1"},{"name":"n","in":"query","required":false,"description":"Mode index n","schema":{"type":"string"},"example":"0"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"mode":"TE10","note":"λg = λ0/√(1−(fc/f)²); phase velocity exceeds c while group velocity (energy/signal speed) stays below c. The guide wavelength is longer than free space.","inputs":{"m":1,"n":0,"width_mm":22.86,"height_mm":10.16,"frequency_ghz":10},"propagating":true,"group_velocity_ms":226346105.331,"phase_velocity_ms":397071192.111,"guide_wavelength_mm":39.707119,"cutoff_frequency_ghz":6.55714,"free_space_wavelength_mm":29.979246},"meta":{"timestamp":"2026-06-05T11:30:30.324Z","request_id":"ba353bc9-e7f7-48dd-b2f9-61f620469623"},"status":"ok","message":"Guide wavelength","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/modes":{"get":{"operationId":"get_v1_modes","tags":["Waveguide"],"summary":"Propagating modes","description":"","parameters":[{"name":"width","in":"query","required":true,"description":"Inner width a (mm)","schema":{"type":"string"},"example":"22.86"},{"name":"height","in":"query","required":true,"description":"Inner height b (mm)","schema":{"type":"string"},"example":"10.16"},{"name":"frequency","in":"query","required":true,"description":"Frequency (GHz)","schema":{"type":"string"},"example":"15"}],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"note":"All modes whose cutoff is at or below the operating frequency propagate. The lowest-cutoff mode is the dominant mode; single-mode operation needs the frequency between the first and second cutoffs.","inputs":{"width_mm":22.86,"height_mm":10.16,"frequency_ghz":15},"mode_count":3,"dominant_mode":"TE10","propagating_modes":[{"mode":"TE10","cutoff_ghz":6.5571},{"mode":"TE20","cutoff_ghz":13.1143},{"mode":"TE01","cutoff_ghz":14.7536}]},"meta":{"timestamp":"2026-06-05T11:30:30.406Z","request_id":"8422bf50-a544-4ae0-a571-7c982aed35c2"},"status":"ok","message":"Propagating modes","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}},"/v1/meta":{"get":{"operationId":"get_v1_meta","tags":["Meta"],"summary":"Spec","description":"","parameters":[],"security":[{"oanorKey":[]}],"responses":{"200":{"description":"OK","content":{"application/json":{"example":{"data":{"notes":"Dimensions in mm, frequencies in GHz. For a > b the dominant mode is TE10, fc = c/(2a). c = 299792458 m/s.","service":"waveguide-api","formulae":{"cutoff":"fc = (c/2)·√((m/a)² + (n/b)²)","velocities":"vp = c/√(1−(fc/f)²) ; vg = c·√(1−(fc/f)²)","guide_wavelength":"λg = λ0/√(1 − (fc/f)²)"},"endpoints":{"GET /v1/meta":"This document.","GET /v1/modes":"All propagating modes at a frequency, with the dominant mode.","GET /v1/cutoff":"Cutoff frequency and wavelength of a TEmn/TMmn mode.","GET /v1/guide-wavelength":"Guide wavelength, phase and group velocity at a frequency."},"description":"Rectangular-waveguide calculator: cutoff frequency of a TE/TM mode, guide wavelength and phase/group velocity at an operating frequency, and the list of propagating modes."},"meta":{"timestamp":"2026-06-05T11:30:30.496Z","request_id":"844c9f59-b999-4165-b8dd-79dd91d2198e"},"status":"ok","message":"Meta","success":true}}}},"401":{"description":"Missing or invalid x-oanor-key header"},"402":{"description":"Active subscription required"},"429":{"description":"Rate-limit or monthly quota reached"},"502":{"description":"Upstream did not respond"}}}}},"x-oanor-pricing":[{"slug":"free","name":"Free","price_cents_month":0,"monthly_call_quota":2550,"rps_limit":2,"hard_limit":true},{"slug":"starter","name":"Starter","price_cents_month":1100,"monthly_call_quota":39500,"rps_limit":6,"hard_limit":true},{"slug":"pro","name":"Pro","price_cents_month":2800,"monthly_call_quota":255000,"rps_limit":15,"hard_limit":true},{"slug":"mega","name":"Mega","price_cents_month":8400,"monthly_call_quota":1740000,"rps_limit":40,"hard_limit":true}],"x-oanor-marketplace-url":"https://www.oanor.com/api/waveguide-api"}