Example values
Select a prepared example, then calculate.
Formula used
Frequency: f = v ÷ λ
Wavelength: λ = v ÷ f
Wave speed: v = f × λ
Frequency describes how many complete wave cycles pass a point each second. Wavelength measures the distance between matching points on successive cycles. Wave speed connects both quantities through the wave equation.
The calculator first converts every entered value into SI units. It then applies the selected rearrangement of the equation. Finally, it converts the answer into your preferred display unit.
How to use this calculator
- Select whether you need frequency, wavelength, or wave speed.
- Choose the wave category for relevant classifications.
- Enter the two known quantities with their units.
- Select a speed preset or enter a custom speed.
- Choose result units, precision, and number format.
- Press Calculate to view results and detailed steps.
- Copy the result, download CSV, or print to PDF.
For light in vacuum, use exactly 299,792,458 meters per second. For sound, speed changes with material and environmental conditions. The air-temperature option provides a practical approximation for ordinary conditions.
Wave-speed reference table
| Medium | Approximate speed | Typical use |
|---|---|---|
| Light in vacuum | 299,792,458 m/s | Electromagnetic calculations |
| Light in air | 299,702,547 m/s | Approximate optical work |
| Sound in air at 20°C | 343.42 m/s | Acoustics |
| Sound in water | 1,482 m/s | Sonar and underwater acoustics |
| Longitudinal sound in steel | 5,960 m/s | Material testing |
Values are representative. Temperature, pressure, composition, direction, and material properties can change actual wave speed.
Electromagnetic spectrum reference
| Region | Approximate wavelength range |
|---|---|
| Radio | Longer than 1 m |
| Microwave | 1 mm to 1 m |
| Infrared | 700 nm to 1 mm |
| Visible light | 380 nm to 700 nm |
| Ultraviolet | 10 nm to 380 nm |
| X-ray | 0.01 nm to 10 nm |
| Gamma ray | Shorter than 0.01 nm |
Understanding frequency from wavelength
Frequency and wavelength move in opposite directions when wave speed stays constant. A shorter wavelength produces a higher frequency. A longer wavelength produces a lower frequency under identical conditions.
Electromagnetic waves in vacuum use the defined speed of light. Radio signals, visible light, ultraviolet radiation, and X-rays all follow this relationship. Their different wavelengths create very different frequencies and practical behaviors.
Sound waves require more care because their speed depends on the medium. Sound usually travels faster through liquids and solids than gases. Temperature also changes sound speed in air enough to affect precise results.
The period is the time required for one complete cycle. It equals one divided by frequency. Angular frequency expresses the same oscillation rate in radians per second.
Unit conversion is essential when wavelength is supplied in nanometers, centimeters, feet, or miles. The calculator converts wavelength to meters before using the formula. Frequency is likewise converted to hertz before related values are determined.
Spectrum labels are useful guides, not perfectly sharp universal boundaries. Different fields sometimes use overlapping or slightly different ranges. The displayed classification should therefore support interpretation rather than replace a technical standard.
Visible color estimates apply only to wavelengths inside the commonly stated human-visible region. Perceived color also depends on intensity, surrounding light, and human vision. Monochromatic wavelength labels cannot fully describe every observed color.
Radio-band classification follows conventional frequency decades from ELF through EHF. Frequencies above that range can still be electromagnetic waves. They are simply outside the calculator’s conventional radio-band table.
Always choose a wave-speed value appropriate for the actual medium. A correct formula cannot compensate for an unsuitable material speed. For high-accuracy work, use measured conditions and authoritative reference data.
Frequently asked questions
1. How do I calculate frequency from wavelength?
Divide wave speed by wavelength after converting both values to compatible units. Using SI units gives frequency directly in hertz.
2. Which speed should I use for light?
Use 299,792,458 m/s for light in vacuum. Use a medium-specific speed when light travels through another material.
3. Which speed should I use for sound?
Select a speed matching the medium and conditions. Air temperature, water properties, and solid composition can affect the answer.
4. Can the calculator find wavelength instead?
Yes. Select Calculate wavelength, then enter frequency and wave speed.
5. Can it calculate wave speed?
Yes. Select Calculate wave speed, then enter frequency and wavelength.
6. What is the relationship between period and frequency?
Period is the reciprocal of frequency. Use T = 1/f to obtain seconds per cycle.
7. What is angular frequency?
Angular frequency equals 2π times ordinary frequency. Its unit is radians per second.
8. Why does shorter wavelength mean higher frequency?
At constant speed, the product of frequency and wavelength must remain equal to wave speed. Reducing wavelength therefore increases frequency.
9. Are spectrum boundaries exact?
No. They are practical conventions, and different technical references may use slightly different boundaries.
10. Why is my result extremely large or small?
Wave quantities often span many powers of ten. Scientific notation helps display those values clearly.
11. Can I save the calculation?
Yes. Use CSV export for data, or print the page and select Save as PDF.