Documentation sections

Doppler Shift Calculator

POSThttps://rftools.io/api/py/v1/calculate

Slug doppler-shift. Calculate Doppler frequency shift for radar and RF applications. Computes the Doppler shift (f_d = 2vf·cos θ/c) given transmit frequency, target velocity, and aspect angle. Also derives velocity from measured shift.

Inputs

Send every one of these in inputs, in the units shown. Most are required: a call without one is refused (400) and costs nothing; one the calculator can do without takes the default shown. An input outside its range is still computed and flagged in the provenance.

Inputs of doppler-shift
Name	Unit	Range	Default	Description
frequencynumber	GHz	0.001 … 300	10	Transmit Frequency
velocitynumber	m/s	0 … 1000000	30	Target Velocity
velocityUnitnumber	none	0 … 1	0	Velocity UnitOne of: 0 m/s · 1 km/h
anglenumber	°	0 … 90	0	Angle between target velocity vector and radar line-of-sight. 0° = head-on (maximum shift), 90° = broadside (no shift)

Outputs

Returned in values, by key. A value that is unbounded or undefined is null.

Outputs of doppler-shift
Field	Unit	Description
f_d_Hzheadline	Hz	Doppler Shift
f_d_kHz	kHz	Doppler Shift
radialVelocity	m/s	Component of target velocity along the radar line-of-sight: v·cos(θ)
velocityPerHz	m/s/Hz	Radar velocity resolution: how much target speed corresponds to 1 Hz of Doppler shift
velocityPerHz_kmh	km/h/Hz	Velocity per Hz (km/h/Hz)

Calling it

Calculate: one call, the request and response in full, and its errors.
Batch: this calculator with others, or a sweep, in one request.
Solve for a target: the value of one input that brings an output to a target.

curl -X POST https://rftools.io/api/py/v1/calculate \
  -H "X-API-Key: $RFTOOLS_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "slug": "doppler-shift",
    "inputs": {
      "frequency": 10,
      "velocity": 30,
      "velocityUnit": 0,
      "angle": 0
    }
  }'

import rftools

client = rftools.Client()  # reads RFTOOLS_API_KEY, or the key `rftools login` saved

result = client.calculate("doppler-shift", {"frequency": 10, "velocity": 30, "velocityUnit": 0, "angle": 0})
print(result.values)
print(result.warnings, result.provenance.formula_ref)

const response = await fetch("https://rftools.io/api/py/v1/calculate", {
  method: "POST",
  headers: {
    "X-API-Key": process.env.RFTOOLS_API_KEY,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
    "slug": "doppler-shift",
    "inputs": {
      "frequency": 10,
      "velocity": 30,
      "velocityUnit": 0,
      "angle": 0
    }
  }),
});
console.log(response.status, await response.json());

package main

import (
	"bytes"
	"fmt"
	"io"
	"net/http"
	"os"
)

func main() {
	body := []byte(`{
	  "slug": "doppler-shift",
	  "inputs": {
	    "frequency": 10,
	    "velocity": 30,
	    "velocityUnit": 0,
	    "angle": 0
	  }
	}`)
	req, err := http.NewRequest("POST", "https://rftools.io/api/py/v1/calculate", bytes.NewReader(body))
	if err != nil {
		panic(err)
	}
	req.Header.Set("X-API-Key", os.Getenv("RFTOOLS_API_KEY"))
	req.Header.Set("Content-Type", "application/json")
	res, err := http.DefaultClient.Do(req)
	if err != nil {
		panic(err)
	}
	defer res.Body.Close()
	out, _ := io.ReadAll(res.Body)
	fmt.Println(res.Status, string(out))
}

application/json

{
  "slug": "doppler-shift",
  "values": {
    "f_d_Hz": 2001.3845711889123,
    "f_d_kHz": 2.0013845711889124,
    "radialVelocity": 30,
    "velocityPerHz": 0.0149896229,
    "velocityPerHz_kmh": 0.05396264244
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:doppler-shift",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Skolnik, Introduction to Radar Systems, 3rd ed., Ch.3",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "frequency": {
          "min": 0.001,
          "max": 300,
          "unit": "GHz"
        },
        "velocity": {
          "min": 0,
          "max": 1000000,
          "unit": "m/s"
        },
        "velocityUnit": {
          "min": 0,
          "max": 1,
          "unit": ""
        },
        "angle": {
          "min": 0,
          "max": 90,
          "unit": "°"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "frequency": 10,
      "velocity": 30,
      "velocityUnit": 0,
      "angle": 0
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "frequency"
      ],
      "msg": "Input should be a valid number, unable to parse string as a number",
      "input": "abc"
    }
  ]
}

An input sent as text. Nothing was counted.

{
  "detail": "More than 120 requests in 60 seconds from this address.",
  "errorKind": "rate_limited",
  "limit": 120,
  "windowSeconds": 60,
  "upgradeUrl": "https://rftools.io/pricing/"
}

Too many requests in a minute, with Retry-After.

Same inputs on the calculator pageDoppler Shift Calculator, at these values