The Astronomy Calculator includes functions that are useful for studying astronomy. Formulae are organized in different tabs to the right as follows:

• Kepler's 3^rd Law formula                             T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula        Small Angle Formula    α = S / D
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• Mass formulas
  • Mass from Luminosity
  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size Formulas
  • Relative Size from Relative Temperature and Luminosity
  • Relative Temperature from Relative Size and Luminosity
  • Relative Luminosity from Relative Temperature and Size
• Wavelength Formulas
  • Velocity from shift in Wavelength and Unshifted Wavelength
  • Wavelength Shift from Wavelength and Speed
  • Blackbody Wavelength from Temperature
  • Blackbody Temperature from Peak Wavelength
  • Photon Energy from Wavelength
  • Photon Wavelength from Energy
• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass

Astronomical Units

Distance Units: The functions have length units that are often defaulted to au (astronomical units) which is the mean distance from the Sun to the Earth.  However, users can automatically change the distance units on both the inputs to the calculator and the solved answers via the pull-down menu.  The  distance units are automatically handled and range from extremely small (nano-meters) to truly astronomical including au, light seconds, light minutes, light years, parsecs, kilo-light years and mega-parses.

Mass Units: The calculator functions have mass units that often default to multiples of the mass of the sun (solar_mass).   However, users can automatically change the mass units on both the inputs to the calculator and the solved answers via the pull-down menu.  The  mass units are automatically handled and range from extremely small (grains) to truly astronomical including Earth masses, Jupiter masses and Solar masses.

Time Units: The calculator functions have time duration units that default to days.   However, users can automatically change the time units on both the inputs to the calculator and the solved answers via the pull-down menu.  The time units are automatically handled and range from extremely small (nanoseconds) to large including weeks, months, years, decades and centuries.  They also include sidereal day and sidereal years.

Related Astro Calculators:

• Hubble's Law
• Kepler's 3^rd Law Calc has Kepler's 3^rd law solved for each parameter.
• Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
• Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
• Orbital Radial Acceleration
• Distance to Barycenter
• Sakuma-Hattori Equation
• Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
• Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
• Ellipse Calculator
• 3D Vector Calculator:
• Drake Equation Calculator
• Seager Equation Calculator
• Friedman Equation Calculator
• Black Hole Mass Calculator
• Black Hole Event Horizon Calculator

Astronomy Calculator's Creator

  Special thanks to Dr. Stephen Spicklemire, Department Chair, Physics &Earth-Space Science, Associate Professor of Physics at the University of Indianapolis.  Dr. Spicklemire created this calculator and all of the underlying equations (functions) to help his astronomy students.  

 "vCalc is awesome for my astronomy students. With vCalc I can give them real problems that would normally require fairly sophisticated reasoning and mathematics, and now they can do the reasoning, because they’re not daunted by the math. It’s great."   Dr. Steve Spicklemire