Hydrogen-line Doppler and LSR calculator

What this calculator does

Neutral hydrogen emits at 1420.405751768 MHz in its own rest frame. Gas moving away from you shows up lower in frequency, gas moving toward you shows up higher, and the shift is the whole reason a hydrogen-line spectrum is worth taking: each peak is a cloud of hydrogen at a particular velocity along your line of sight. To compare your spectrum with anyone else's, or with a survey, you have to take out your own motion first. That's the local standard of rest correction, and it's the step most first spectra skip.

The conversion

Hydrogen-line work reports velocities in the radio convention, which is linear in frequency:

The optical convention, v = c(f₀ − f)/f, divides by the observed frequency instead. The two differ by v²/c, about 0.03 km/s at 100 km/s, but surveys and papers quote radio velocities, so that's the number we lead with. A 1 kHz shift is 0.211 km/s.

The LSR correction, in three parts

The frequency you measure includes three motions of your own that have nothing to do with the gas. The calculator projects each onto the direction you were pointing and adds them:

• Earth's rotation. At most about 0.47 km/s, at the equator, for a target on the eastern or western horizon. Small, but it changes through the night.
• Earth's orbit. About 30 km/s around the Sun, so up to ±30 km/s along your line of sight depending on the season. This is the big one, and why a spectrum taken in spring and one taken in autumn won't line up without it.
• The Sun's motion relative to its neighbours. The standard (kinematic) local standard of rest assumes the Sun moves at 20 km/s toward RA 18h, Dec +30° (B1900). That's a convention, not a measurement of anything in your data, which is exactly why everyone uses the same one.

We use a low-precision solar ephemeris for Earth's orbital velocity rather than a full planetary theory. Checked against a full barycentric reduction it lands within about 0.1 km/s, which is a fraction of one channel on any amateur spectrum we know of.

Worked example

Say you're at 40° N, 75° W, pointed at Galactic longitude 30° on the plane, and at 03:00 UTC on 6 October 2026 you see a peak at 1420.000 MHz. That's 405.8 kHz below rest, a topocentric radio velocity of +85.6 km/s. Projected onto that direction, Earth's orbit contributes −27.9 km/s, the Sun's motion +16.6 km/s and rotation −0.3 km/s, a total correction of −11.7 km/s. The peak is at +74.0 km/s relative to the LSR. At l = 30° the inner-Galaxy gas reaches out to roughly +100 km/s, so that's a believable number. At that moment, rest-frame hydrogen at zero LSR velocity would appear at 1420.3504 MHz, which is where you'd centre the SDR.

Notice the target was only about 18° up in the west-southwest at that time. The calculator shows altitude so you can catch the case where the numbers are fine and the sky isn't.

Things that trip people up

• Longitude sign. East is positive. A site in North America has a negative longitude. Get this wrong and the rotation term and the altitude go wrong; the orbit and solar terms don't care.
• Local time. Enter UTC. The orbital term moves slowly, but altitude and rotation depend on the hour.
• Your SDR's frequency error. An RTL-class dongle without a TCXO can be off by tens of ppm, and 1 ppm at 1420 MHz is 1.4 kHz, or 0.3 km/s. The V3 has a 1 ppm TCXO; older dongles need a correction measured against a known carrier before any of this means much.
• Sign of the correction. We add it to the topocentric velocity. If you're checking against another program, make sure it's reporting the same thing and not the observer's velocity with the opposite sign.