Documentation sections

Radar Range Equation Calculator

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

Slug radar-range-equation. Calculate maximum radar detection range from peak power, antenna gain, RCS, noise figure, and bandwidth using the radar equation. Free, instant results.

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 radar-range-equation
Name	Unit	Range	Default	Description
peakPowernumber	kW	at least 0.001	100	Peak transmitter output power in kilowatts
gainnumber	dBi	at least 0	30	Transmit/receive antenna gain (same antenna assumed)
frequencynumber	GHz	at least 0.1	3	Frequency
rcsnumber	m²	at least 0.001	1	Target radar cross section in square meters
noiseFigurenumber	dB	at least 0	6	Receiver noise figure in dB
bandwidthnumber	MHz	at least 0.001	1	Receiver noise bandwidth in MHz
pdnumber	none	0.01 … 0.999	0.9	Required probability of detecting the target; Albersheim's equation holds for 0.1 to 0.9
pfanumber	none	1e-12 … 0.1	0.000001	Allowed probability that noise alone crosses the threshold, e.g. 1e-6; Albersheim's equation holds for 1e-7 to 1e-3
pulsesnumber	none	1 … 8096	1	Pulses integrated noncoherently before detection; 1 is a single pulse

Outputs

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

Outputs of radar-range-equation
Field	Unit	Description
maxRangeheadline	km	Maximum Detection Range
snrAtMaxRange	dB	The single-pulse SNR that P_d and P_fa need (Albersheim's equation, nonfluctuating target); maximum range is where the echo reaches it
receivedPower	dBm	Received Power at 1 km

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": "radar-range-equation",
    "inputs": {
      "peakPower": 100,
      "gain": 30,
      "frequency": 3,
      "rcs": 1,
      "noiseFigure": 6,
      "bandwidth": 1,
      "pd": 0.9,
      "pfa": 0.000001,
      "pulses": 1
    }
  }'

import rftools

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

result = client.calculate("radar-range-equation", {
    "peakPower": 100,
    "gain": 30,
    "frequency": 3,
    "rcs": 1,
    "noiseFigure": 6,
    "bandwidth": 1,
    "pd": 0.9,
    "pfa": 0.000001,
    "pulses": 1,
})
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": "radar-range-equation",
    "inputs": {
      "peakPower": 100,
      "gain": 30,
      "frequency": 3,
      "rcs": 1,
      "noiseFigure": 6,
      "bandwidth": 1,
      "pd": 0.9,
      "pfa": 0.000001,
      "pulses": 1
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "radar-range-equation",
	  "inputs": {
	    "peakPower": 100,
	    "gain": 30,
	    "frequency": 3,
	    "rcs": 1,
	    "noiseFigure": 6,
	    "bandwidth": 1,
	    "pd": 0.9,
	    "pfa": 0.000001,
	    "pulses": 1
	  }
	}`)
	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": "radar-range-equation",
  "values": {
    "maxRange": 35.23371147158789,
    "snrAtMaxRange": 13.11454449432279,
    "receivedPower": -32.98230695649758
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:radar-range-equation",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "Albersheim, A closed-form approximation to Robertson's detection characteristics, Proc. IEEE 69(7), 1981, p. 839; Skolnik, Introduction to Radar Systems, 3rd ed. (2001), Fig. 2.7",
    "assumptions": [
      {
        "code": "albersheim-nonfluctuating",
        "text": "The required SNR is Albersheim's closed form for a nonfluctuating target with N pulses integrated noncoherently, within 0.2 dB of Robertson's curves for 0.1 ≤ P_d ≤ 0.9, 10⁻⁷ ≤ P_fa ≤ 10⁻³ and 1 ≤ N ≤ 8096."
      },
      {
        "code": "lossless-290-k",
        "text": "No system, propagation or processing losses are included, and the noise temperature is 290 K."
      }
    ],
    "validRange": {
      "status": "inside",
      "bounds": {
        "peakPower": {
          "min": 0.001,
          "max": null,
          "unit": "kW"
        },
        "gain": {
          "min": 0,
          "max": null,
          "unit": "dBi"
        },
        "frequency": {
          "min": 0.1,
          "max": null,
          "unit": "GHz"
        },
        "rcs": {
          "min": 0.001,
          "max": null,
          "unit": "m²"
        },
        "noiseFigure": {
          "min": 0,
          "max": null,
          "unit": "dB"
        },
        "bandwidth": {
          "min": 0.001,
          "max": null,
          "unit": "MHz"
        },
        "pd": {
          "min": 0.01,
          "max": 0.999,
          "unit": ""
        },
        "pfa": {
          "min": 1e-12,
          "max": 0.1,
          "unit": ""
        },
        "pulses": {
          "min": 1,
          "max": 8096,
          "unit": ""
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "peakPower": 100,
      "gain": 30,
      "frequency": 3,
      "rcs": 1,
      "noiseFigure": 6,
      "bandwidth": 1,
      "pd": 0.9,
      "pfa": 0.000001,
      "pulses": 1
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "peakPower"
      ],
      "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 pageRadar Range Equation Calculator, at these values