Telescope, orbit and stargazing math.
Free astronomy tools: telescope magnification, focal ratio, exit pupil, pixel scale, escape velocity, orbital period, redshift and stellar luminosity calculators. All 20 tools below are free, run entirely in your browser, and need no sign-up.
Free telescope magnification calculator. Divide telescope focal length by eyepiece focal length to find power, plus your maximum useful magnification from aperture.
Free telescope focal ratio calculator. Find the f-number of a telescope from focal length and aperture, or solve for the focal length needed to hit a target f-ratio.
Free telescope resolving power calculator. Find the Dawes and Rayleigh limits in arcseconds from your aperture to judge the finest double star split your scope can show.
Free telescope exit pupil calculator. Find the exit pupil in millimeters from aperture and magnification, or from eyepiece focal length and focal ratio, to match your eye.
Free CCD pixel scale calculator for astrophotography. Find arcseconds per pixel from your camera pixel size and telescope focal length to check if you are matched to seeing.
Free angular size calculator. Find how large an object appears in the sky in degrees, arcminutes and arcseconds from its true diameter and distance, or solve for size.
Free escape velocity calculator. Find the speed needed to escape a planet, moon or star from its mass and radius using the square root of two GM over r.
Free orbital period calculator. Find how long a satellite or moon takes to orbit a body from the central mass and orbit radius using Newton form of Kepler third law.
Free Kepler third law calculator for the solar system. Convert between orbital period in years and semi-major axis in astronomical units where P squared equals a cubed.
Free Schwarzschild radius calculator. Find the event horizon size of a black hole from its mass using two GM over c squared, in meters, kilometers and solar masses.
Free redshift velocity calculator. Convert a spectral redshift z into recession velocity using both the simple Doppler and relativistic formulas, in km/s and fraction of light.
Free absolute magnitude calculator. Convert between apparent and absolute magnitude using the distance modulus, and solve for distance in parsecs and light years.
Free star brightness ratio calculator. Convert a magnitude difference between two stars into how many times brighter one is using the Pogson ratio of 2.512.
Free light travel time calculator. Find how long light takes to cross a distance and convert light years, light minutes and light seconds into kilometers and miles.
Free parsec to light year converter. Convert between parsecs, light years, astronomical units and kilometers for astronomical distances, both directions instantly.
Free limiting magnitude calculator. Estimate the faintest star your telescope can show from its aperture, so you know what deep sky targets are within reach.
Free planet orbital speed calculator. Find how fast a planet moves around the Sun from its orbital radius using the vis-viva circular speed formula, in km/s and mph.
Free surface gravity calculator. Find the gravitational acceleration at the surface of a planet, moon or star from its mass and radius using g equals GM over r squared.
Free Wien law calculator. Find the peak emission wavelength of a star or blackbody from its temperature, and see the color band it falls in, using the displacement law.
Free stellar luminosity calculator. Find a star total energy output from its radius and surface temperature with the Stefan-Boltzmann law, in watts and solar luminosities.
Yes. Every astronomy tool on yourhack.ai is completely free, with no sign-up and no usage limits.
Yes. They run in any modern web browser on phone, tablet or desktop. There is nothing to install.
Yes. These tools run entirely in your browser, so nothing you enter is uploaded to a server.
There are currently 20 free astronomy tools here, and we add more regularly.