Frequency Calculator

Frequency: How many cycles happen each second. The standard unit is hertz, written as Hz.

Period: The time for one full cycle. Frequency and period are reciprocals, so f = 1/T.[2]

Wavelength: The distance covered by one full wave cycle. In wave modes, it depends on the wave speed in the same medium.[1]

Wave speed: How fast the wave travels through a medium such as air or vacuum. A different medium can change the result in wave calculations.[1]

Angular frequency: A rotation-style way to express how fast a cycle repeats, measured in rad/s. It is related to ordinary frequency by omega = 2 pi f.

Rotational speed (rpm): Revolutions per minute. Divide rpm by 60 to convert to hertz.

Mistake: Entering Period (selected unit) as 20 when you really mean 20 ms, but leaving Period unit on seconds.
Fix: Change Period unit to milliseconds (ms), or enter the value in seconds instead.

Mistake: Typing Angular frequency (rad/s) into Frequency (selected unit).
Fix: Use the mode Frequency from angular frequency, then enter the number in Angular frequency (rad/s).

Mistake: Using Light in vacuum for a sound problem in Wave medium preset.
Fix: In wave modes, pick the medium that matches the problem, or use Custom wave speed and enter Wave speed (selected unit) yourself.

Mistake: Mixing length units by entering Wavelength (selected unit) as 500 but forgetting that Wavelength unit is nm or mm.
Fix: Check that Wavelength unit matches the number you typed before you calculate.

Mistake: Expecting Rotational speed (rpm) and Frequency in hertz to be the same number.
Fix: Remember that 1 Hz = 60 rpm, so use the rpm modes when your starting value is in revolutions per minute.

Mistake: Entering 0 or a negative value for Frequency (selected unit), Period (selected unit), Wavelength (selected unit), Wave speed (selected unit), Angular frequency (rad/s), or Rotational speed (rpm).
Fix: Enter a positive number greater than 0 for the active mode, because these formulas use physical magnitudes and some divide by that value.

• This calculator uses ideal formula relationships. Real systems can differ because of friction, damping, measurement error, or changing conditions.
• Wave results depend on the wave speed in the same medium as the wave. If the medium or speed is wrong, the wavelength or frequency result will also be wrong.
• The Sound in air at 20 C preset is a reference assumption, not a universal value. Actual sound speed in air changes with conditions such as temperature.
• The Light in vacuum preset should only be used for light in vacuum, not for sound or for light traveling through materials.
• Inputs used in denominators must be greater than zero, so zero or negative period, frequency, wavelength, wave speed, angular frequency, or rpm are rejected for the modes that use them.
• Outputs are positive magnitudes only for these formulas. The tool does not model direction, phase sign, or negative rotation conventions.
• Displayed values are rounded by the chosen Significant figures and Display format, so the shown result may be a rounded version of the internal calculation.

Core formulas

The calculator first converts your entered value into standard base units, such as seconds, hertz, meters, and meters per second. Then it applies the matching formula for the selected mode.

f = 1 / T

T = 1 / f

f = v / λ

λ = v / f

ω = 2 * pi * f

f = ω / (2 * pi)

f = rpm / 60

rpm = 60 * f

Unit conversions used before solving

1 ms = 0.001 s

1 us = 0.000001 s

1 kHz = 1000 Hz

1 MHz = 1000000 Hz

1 GHz = 1000000000 Hz

1 THz = 1000000000000 Hz

1 cm = 0.01 m

1 mm = 0.001 m

1 um = 0.000001 m

1 nm = 0.000000001 m

1 km = 1000 m

Medium preset logic

In wave modes, the Wave medium preset can fill Wave speed automatically. The sound-in-air preset uses 343 m/s as a reference value for air at about 20 C.[1] If you choose a preset, the calculation uses that preset speed so the math matches the stated assumption.

Worked mini-example

Example 1:

if Period (selected unit) is 0.02 s, then frequency is 1 / 0.02 = 50 Hz. That also gives angular frequency 2 x pi x 50 = 314.1593 rad/s and rotational speed 60 x 50 = 3000 rpm.[2]

Example 2:

if Wave speed (selected unit) is 343 m/s and Wavelength (selected unit) is 2 m, then frequency is 343 / 2 = 171.5 Hz. Because the wavelength formula depends on the medium, changing the wave speed would change the answer.[1]

How to interpret the outputs

Calculated value is the main answer for your selected mode, and Primary unit tells you the unit to copy into homework or lab notes. The extra outputs are cross-checks. For example, a higher Frequency in hertz means a shorter Period in seconds, while a larger Wavelength in meters at the same wave speed means a lower frequency.

Assumptions used by the calculator

The formulas assume repeating cycles and positive physical magnitudes. Results can differ from real measurements if the system is not perfectly steady, if the wave speed changes, or if the wrong medium is chosen.