Astrophysics & Cosmology
Every astrophysics & cosmology calculator on CalcEngines — each with its formula, a worked example, the standard it follows and the assumptions it makes.
10 calculators in this section
- Drake Equation Calculator: What It Does and Does Not Tell YouN = R*·fp·ne·fl·fi·fc·L multiplies seven factors to get the number of civilisations we could hear from. Three of them have been measured. Four of them have never been measured at all, and the answer moves by a factor of ten every time one of those four does. This page does the arithmetic and shows you exactly where the answer comes from.
- Hawking Temperature Calculator: How Cold, and How Long to EvaporateA black hole glows, very faintly, at a temperature set entirely by its mass — and the bigger it is, the colder it gets. Put in a mass and this gives you the Hawking temperature, the power it radiates, and the evaporation lifetime. For a black hole the mass of the Sun that lifetime is 2×1067 years. The absurdity of that number is the lesson.
- Hubble’s Law and Age of the Universe Calculatorv = H₀d, with the Hubble time 1/H₀ beside it — and a clear statement of why that is only an estimate of the age. The two best measurements of H₀ disagree: 67.4 from the cosmic microwave background and 73.04 from the distance ladder. Both are in the box, and this page does not pretend to know which is right.
- Light Year, Parsec and Astronomical Unit ConverterEvery astronomical distance unit, both ways, from exact definitions rather than rounded textbook factors. The parsec is 648 000/π au exactly, the au is 149 597 870 700 m exactly and the light year is 9 460 730 472 580 800 m exactly — so 1 pc = 3.261 564 ly is a definition, not a measurement.
- Luminosity and Magnitude Calculator: Apparent, Absolute and Distance ModulusApparent magnitude and distance in, absolute magnitude out — plus the luminosity, the irradiance reaching us and the distance modulus. The scale runs backwards and it is logarithmic: five magnitudes is a factor of exactly 100 in brightness, and the brighter star has the smaller number. Both conventions are built in here.
- Olbers’ Paradox Calculator: Why the Night Sky Is DarkIn a universe that was infinite, unchanging and eternally old, every line of sight would end on the surface of a star and the whole sky would blaze. It does not. Set the age you want to assume, switch expansion and dust on and off, and this page tells you which assumption actually fails — and it is not the one most people name.
- Radiation Pressure Calculator: Solar Sails, P = I/c and 2I/cLight carries momentum, so it pushes. Absorb it and the pressure is I/c; reflect it and the pressure is 2I/c, because the light leaves again going the other way. Sunlight at the Earth gives nine millionths of a pascal on a mirror. This page works out the pressure, the force on a sail and the acceleration it produces.
- Redshift and Recession Velocity Calculator: z, v = cz and the Relativistic FormRest wavelength and observed wavelength in; the redshift z out, with both recession speeds beside it — the school approximation v ≈ cz and the relativistic Doppler form — and the percentage by which the first one overstates the second. At z = 1 the approximation returns exactly c, which is the clearest sign that it has broken.
- Schwarzschild Radius Calculator: How Small Before It Is a Black HolePut in a mass and the radius it actually has, and this works out the Schwarzschild radius — the size it would have to be squeezed to before it became a black hole — and then the thing worth knowing: how many factors of ten of squeezing that is. The Sun needs five. You need about twenty-five.
- Stellar Parallax Distance Calculator: Parallax Angle to Parsecs and Light Yearsd = 1/p, with d in parsecs and p in arcseconds — the only distance in astronomy measured by geometry alone, with no assumption about the star. Enter the parallax and its uncertainty and this page also gives you the distance range that uncertainty allows, which is where the method stops working.