Astronomy calculators
Six calculations that turn what a telescope measures (brightness, angle, the speed of stars) into what we want to know (distance, size, mass). Each one shows its formula so you can check the working, not just the answer.
1 · Distance modulus
m − M ↔ distanceEdit the modulus or the distance; the other updates. Typing m and M fills in the modulus.
2 · Angular size ↔ real size
small-angle formulaExample loaded: the Moon, about 0.518° wide at 384,400 km. Its measured diameter is 3,474 km.
3 · How far apart are they really?
law of cosinesTwo objects that look close together on the sky can be far apart along the line of sight. Give each one's distance and the angle between them.
Both distances in the same unit (Mpc, kpc, ly…); the answer comes out in that unit.
4 · Surface brightness
mag per arcsec²How bright each square arcsecond of an object looks: the average inside the radius that holds half the light. Surface brightness does not change with distance, because the light and the area both shrink with the square of distance.
Luminosity is converted with the Sun's absolute V magnitude, M☉ = 4.83. Bigger numbers mean fainter: 5 magnitudes is a factor of exactly 100.
5 · Mass from moving stars
dynamical massStars in a cluster or small galaxy move faster when there is more mass holding them in. Measuring their spread of speeds (velocity dispersion σ) weighs everything inside the half-light radius, dark matter included.