---
title: "Relativistic Doppler Shift calculator — AperiOptic"
description: "Wavelength shift for source moving along line of sight. Free online optics calculator, with the formula and code snippets."
url: "https://aperioptic.com/calculators/relativistic-doppler-shift"
---

# Relativistic Doppler Shift calculator

Wavelength shift for source moving along line of sight.

Category: [Spectroscopy](https://aperioptic.com/calculators)

Formula: `β = v/c · λ = λ₀ · √((1+β)/(1-β))`

## Inputs

| Input | Parameter | Unit | Default |
| --- | --- | --- | --- |
| Rest λ₀ | `lam0` | nm | 656.28 |
| Velocity v (receding +) | `v` | m/s | 30000 |

## Result with the default inputs

- Observed λ: 656.3457 nm
- Δλ: 0.0657 nm
- Redshift z: 1.0007e-4
- β = v/c: 1.0007e-4

Open it with your own values: put each input in the address as a parameter, for example [`/calculators/relativistic-doppler-shift?lam0=656.28`](https://aperioptic.com/calculators/relativistic-doppler-shift?lam0=656.28). A unit other than the listed one goes in `<parameter>_unit`.

Read more: [Wikipedia: Relativistic Doppler effect](https://en.wikipedia.org/wiki/Relativistic_Doppler_effect)

[All optics calculators](https://aperioptic.com/calculators)

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The interactive page: https://aperioptic.com/calculators/relativistic-doppler-shift (AperiOptic runs in the browser; free, no account). Every page of the site as Markdown: https://aperioptic.com/llms.txt