Redshift Calculator
Galaxy redshift, velocity, and Hubble distance.
What it does
Redshift stretches light across expanding space: distant galaxies redden as wavelengths grow, encoding recession speed and rough distance in one ratio. Nearby blueshifts approach instead.
The tool above takes observed with rest wavelengths. It returns z, velocity, and Hubble distance.
The default 658 over 656.3 gives z 0.0026 receding at 777 km/s from 36 million light years out. The 505 over 500.7 case gives 0.0086 at 2575.
Cosmology tutorials define z from wavelength ratios with light speed behind velocities. Telescope science materials repeat the Hubble division for distances.
Low redshift linear math bends at cosmic scales where expansion history matters. Peculiar motions jitter nearby readings while distant flow obeys Hubble.
How to use
- Type observed nm.
- Type rest nm.
- Read z first.
- Read velocity beside it.
- Read Hubble distance last.
- Respect low z limits.
Formula
- obs
- Seen wavelength in nm.
- rest
- Lab rest wavelength in nm.
- z
- Dimensionless shift.
Cosmology references define redshift from rest and observed wavelengths with recession near light speed times z. Space telescope science materials mirror the same Hubble law distance division. Negative shifts report approaching with absolute speeds.
Worked example
Example: shifted H-alpha
Defaults: 658 observed, 656.3 rest.
- Line: H-alpha rest 656.3 nm, seen 658.
- Shift: (658 minus 656.3) / 656.3 = 0.0026.
- Speed: 0.0026 x 299792 = 777 km/s away.
- Distance: 777 / 70 x 3.26 = 36 million light years.
- Check: positive z means receding red.
- Tool shows z = 0.0026, 777 km/s receding, 36 million light years (Hubble).
Reference table
| Observed | z | Speed |
|---|---|---|
| 658 | 0.0026 | 777 km/s |
| 660 | 0.0056 | 1690 km/s |
| 650 | minus 0.0096 | 2878 km/s approaching |
| 505/500.7 | 0.0086 | 2575 km/s |
Limits
- Low z linear math.
- Hubble constant assumed 70.
- Peculiar motions unread.
- No relativistic corrections.
Common mistakes
- Reading z as speed directly.
- Trusting nearby distances.
- Ignoring blueshift signs.
- Mixing nm with angstroms.
- Overstating Hubble precision.
Try it yourself
Quick checks. Answers sit tucked under each question.
505 over 500.7?
z 0.0086 receding at 2575 km/s from 120 Mly.
650 over 656.3?
Negative z means approaching: check the lines.
Rest 0?
Zero rest divides nothing: enter rest above 0.
Questions
Redshift math?
Observed minus rest over rest. Positive reddens away, negative blueshifts near.
Speed from z?
Light speed times z at low z: 0.0026 runs 777 km/s.
Distance?
Velocity over H0 times 3.26 million light years per megaparsec.
Exact distances?
No, peculiar motions and gravity bend nearby readings. Distant Hubble flow rules.
Blueshift?
Yes, blueshifts read negative z with approaching velocities.
Just Doppler?
No, cosmic expansion stretches light itself; Doppler analogies limp past low z.