Why use the relativistic formula instead of the classical one?

At velocities above roughly 1% of c, the classical formula gives noticeable errors. The relativistic formula is exact for all velocities and reduces to the classical result at low speeds, so it is always the safer choice.

What does a positive velocity mean here?

Positive velocity means the source is moving away from the observer (recession). This increases the observed wavelength — a redshift. Negative velocity means the source is approaching, decreasing the wavelength — a blueshift.

What is the valid range for velocity?

Velocity must be strictly between −1 and +1 (exclusive) because nothing with mass can reach the speed of light (v/c = ±1). The tool enforces this limit.

How is the Doppler factor calculated?

The relativistic Doppler factor is √((1 + β) / (1 − β)) where β = v/c. Observed wavelength = source wavelength × factor; observed frequency = source frequency / factor.

Can I enter frequencies in other units?

The tool works in THz for frequency and nm for wavelength, which are the natural units for visible and near-visible light. Convert first if your source is in other units (e.g. 1 THz = 1000 GHz).

Doppler Shift Calculator (Light)

Enter a source wavelength (or frequency) and velocity relative to c to compute the relativistically shifted observed wavelength and frequency.

Source Light

Source wavelength (nm)

Visible light: ~380–700 nm

Relative velocity (v/c)

Range: −0.9999 to 0.9999 · Positive = receding (redshift), negative = approaching (blueshift)

Observed Light

Enter source values and velocity, then click Calculate.

Relativistic Doppler Formula

Doppler factor

k = √((1 + β) / (1 − β))

Observed wavelength

λ_obs = λ_src × k

Observed frequency

f_obs = f_src / k

β = v/c (positive = source receding). Valid for all velocities |β| < 1.

Copied!

Summary

This tool applies the relativistic Doppler formula to calculate the observed wavelength and frequency of light when source and observer move relative to each other. Unlike the classical approximation, the relativistic version is accurate at any speed. Enter wavelength or frequency along with a velocity fraction of c and get instant results including shift magnitude and direction.

How it works

User enters source wavelength in nm or source frequency in THz.
User enters relative velocity β = v/c (range −0.9999 to 0.9999).
The tool computes the relativistic Doppler factor k = √((1 + β) / (1 − β)).
Observed wavelength λ_obs = λ_source × k; observed frequency f_obs = f_source / k.
Shift percentage and direction (redshift / blueshift) are displayed alongside a visible-spectrum color indicator.

Use cases

Estimate the redshift of a star or galaxy receding at a known fraction of c.
Check how much a laser frequency blue-shifts for an approaching detector.
Teach or study special-relativity Doppler effects in physics coursework.
Verify hand-calculated relativistic Doppler answers against a reference tool.
Explore what velocity would shift a visible wavelength outside the visible range.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu