Waves & Optics Calculators: Light, Lenses and Sound

This collection of waves and optics calculators helps you solve the most common problems involving light, sound, and wave motion. Use the Wave Speed calculator to find how fast a wave travels from its frequency and wavelength, or the Doppler Effect calculator to determine the perceived frequency shift of a moving source or observer — a key concept in acoustics and radar.
For geometric optics, the Lens Equation and Magnification calculators handle image distance, focal length, and image size, while Snell's Law computes refraction angles as light passes between media. These tools are ideal for physics students, engineers, optical designers, and anyone working with lenses, prisms, or wave phenomena.

Mach Number

Enter an object's speed and the local speed of sound to get its Mach number, speed unit conversions, Mach cone angle, and the flow regime (subsonic, transonic, supersonic, hypersonic).

Speed of Sound in Air

Enter air temperature, humidity and atmospheric pressure to instantly find how fast sound travels in air. Results are given in m/s, km/h, ft/s, mph and knots, with the humidity effect and reference values.

Wave Speed

Calculate wave speed, wavelength or frequency from the other two values using the wave equation v = f·λ. Enter any two quantities, pick your units, and the missing one is solved instantly.

Beat Frequency

Enter the frequencies of two nearby tones in Hz, kHz, MHz or rpm to find the beat frequency, beat period, perceived pitch and interval in cents. Great for tuning instruments by ear.

Double-Slit Interference

Calculate the fringe spacing and the position of bright fringes in Young's double-slit experiment. Enter the wavelength, slit separation, screen distance and fringe order.

Malus's Law

Calculate how much linearly polarized light passes through a polarizer using Malus's law. Enter the incident intensity and the angle between the polarization direction and the analyzer axis.

Sound Intensity Level

Convert sound intensity in W/m² to a decibel (dB) level using the standard hearing threshold reference of 10⁻¹² W/m². Optionally compare two sounds to see their level difference.

Snell's Law

Enter the angle of incidence and the refractive indices of the two media to find the angle of refraction from Snell's law. The calculator also reports the critical angle and warns you when total internal reflection occurs.

Diffraction Grating

Calculate the diffraction angle of a spectral line from its wavelength, grating line density and diffraction order. Enter the values and the calculator solves the grating equation and lists all observable orders.

Lens Equation

Solve the thin lens equation 1/f = 1/do + 1/di for image distance, object distance or focal length. Enter any two known values and get the third, plus image type, magnification and image height.

Magnification

Enter the object and image heights, or their distances from a lens or mirror, to get the linear magnification, the image size, and whether the image is upright or inverted.

Wien's Displacement Law

Enter a blackbody's temperature to find the wavelength where it emits the most radiation (or enter a peak wavelength to find the temperature). Results include unit conversions, the spectral band, and the peak frequency.

Doppler Effect

Calculate the frequency you hear when a sound source or observer is moving. Enter the source frequency, both speeds and the wave speed to get the observed pitch for approaching and receding motion.