Documentation sections

Rise Time to Bandwidth Calculator

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

Slug rise-time-bandwidth. Convert digital rise time to signal bandwidth. Get the knee frequency, 3 dB bandwidth, IPC-2251 spectral bandwidth, and the highest significant harmonic of your clock.

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 rise-time-bandwidth
Name	Unit	Range	Default	Description
riseTimenumber	ps	at least 1	500	Rise Time
riseTimeConventionnumber	none	0 … 1	0	Datasheets quote either 10–90% or 20–80%. The 1.585 conversion is the single-pole value — the largest in common use, so it is the least conservative choice for sizing an interconnectOne of: 0 10–90% · 1 20–80%
clockFrequencynumber	MHz	at least 0	100	Optional — used to report how many harmonics fall below the knee frequency; 0 leaves it out

Outputs

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

Outputs of rise-time-bandwidth
Field	Unit	Description
kneeFrequencyheadline	MHz	0.5/t_r — above this a digital edge carries negligible energy
bandwidth3dB	MHz	ln(9)/(2π·t_r) = 0.3497/t_r, the exact single-pole result
spectralBandwidth	MHz	Spectral Bandwidth (1/πt_r)
harmonicNumber	×f_clk	Highest Significant Harmonic
riseTime1090	ps	Rise Time (10–90% equivalent)

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": "rise-time-bandwidth",
    "inputs": {
      "riseTime": 500,
      "riseTimeConvention": 0,
      "clockFrequency": 100
    }
  }'

import rftools

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

result = client.calculate("rise-time-bandwidth", {"riseTime": 500, "riseTimeConvention": 0, "clockFrequency": 100})
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": "rise-time-bandwidth",
    "inputs": {
      "riseTime": 500,
      "riseTimeConvention": 0,
      "clockFrequency": 100
    }
  }),
});
console.log(response.status, await response.json());

package main

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

func main() {
	body := []byte(`{
	  "slug": "rise-time-bandwidth",
	  "inputs": {
	    "riseTime": 500,
	    "riseTimeConvention": 0,
	    "clockFrequency": 100
	  }
	}`)
	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": "rise-time-bandwidth",
  "values": {
    "kneeFrequency": 999.9999999999999,
    "bandwidth3dB": 699.3983051321196,
    "spectralBandwidth": 636.6197723675814,
    "harmonicNumber": 9.999999999999998,
    "riseTime1090": 500
  },
  "warnings": [],
  "errors": [],
  "provenance": {
    "method": "calculator:rise-time-bandwidth",
    "version": "api@3f2c1a9b04de",
    "formulaRef": "H. Johnson & M. Graham, \"High-Speed Digital Design: A Handbook of Black Magic\", Prentice Hall 1993, §1.3; IPC-2251",
    "assumptions": [],
    "validRange": {
      "status": "inside",
      "bounds": {
        "riseTime": {
          "min": 1,
          "max": null,
          "unit": "ps"
        },
        "riseTimeConvention": {
          "min": 0,
          "max": 1,
          "unit": ""
        },
        "clockFrequency": {
          "min": 0,
          "max": null,
          "unit": "MHz"
        }
      },
      "outside": [],
      "model": null
    },
    "computedAt": "2026-09-24T14:05:11.003Z",
    "inputs": {
      "riseTime": 500,
      "riseTimeConvention": 0,
      "clockFrequency": 100
    },
    "seed": null,
    "elapsedSeconds": 0.003
  }
}

{
  "detail": [
    {
      "type": "float_parsing",
      "loc": [
        "body",
        "inputs",
        "riseTime"
      ],
      "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 pageRise Time to Bandwidth Calculator, at these values