Wave Equation Calculator
Wave equation calculator (v = fλ): solve for wave speed, frequency or wavelength in SI units, with a US/imperial readout. Curriculum-aligned.
Wave Equation Calculator
Enter any two values and leave the third blank — the calculator solves for it. Results are in SI units, with a US/imperial readout below.
- Curriculum
- English (global) — Cambridge International + IB
- Built against
- Cambridge IGCSE Physics 0625 + IB Diploma (2023–2025) — Waves
- Unit system
- SI primary; US/imperial readout below
- First published
- 2 Jun 2026
- Last updated
- 4 Sep 2026
View authoritative scientific sources
- NIST SP 811 (2008), §3 — units & conversions
- BIPM SI Brochure, 9th edition (2019)
- Wave — Encyclopædia Britannica
⚠️ Educational use only — see full disclaimer
EDUCATIONAL USE DISCLAIMER
This calculator is provided for educational and reference purposes only. It is not a substitute for instruction from a qualified teacher, your prescribed textbook, or your school's official curriculum materials.
When preparing for examinations, always cross-check our calculations and notation against your current syllabus and your teacher's guidance. Syllabus conventions and accepted notation vary between curricula and may change between examination years.
If you believe any calculation, notation, or curriculum reference in this tool is inaccurate, please let us know via the feedback button. We review feedback promptly and update tools when verified corrections are needed.
RECATOOLS accepts no liability for academic, examination, professional, or research outcomes arising from use of this tool.
How to Use the Wave Equation Calculator
Pick your curriculum
Use the curriculum pills above to match your syllabus (Cambridge/IB, 高考 or SPM). Terminology and the whole page follow your selection.
Enter any two values
Type two of wave speed, frequency and wavelength — leave the one you want to find blank. Each field has a unit selector (Hz, kHz, MHz; m, cm, mm).
Read the SI result
The answer is shown in SI units — metres per second (m/s), hertz (Hz), metres (m), with a dimmed US/imperial readout for speed and wavelength.
Check against your syllabus
The Tool Information block shows exactly which syllabus this is built against. Spot something off? Use the feedback button.
The Wave Equation, in Your Curriculum's Words
Wave Equation (speed = frequency × wavelength)
Example: A wave has a frequency of 50 Hz and a wavelength of 2.0 m. Find its wave speed.
Given: f = 50 Hz, λ = 2.0 m. Using v = fλ:
v = 50 × 2.0 = 100 m/s
The wave equation relates a wave's speed to its frequency and wavelength: v = fλ. Speed is in metres per second (m/s), frequency in hertz (Hz) — cycles per second — and wavelength in metres (m). Rearranged, the same relation gives frequency (f = v / λ) or wavelength (λ = v / f). The calculator solves for whichever value you leave blank.
For a wave travelling in the same medium, the speed is fixed; so if the frequency increases, the wavelength decreases in inverse proportion. This is why high-frequency sound has a short wavelength. SI is always the primary result, with a dimmed US/imperial readout for speed and wavelength. All calculation happens in your browser — nothing is uploaded, and it works offline once loaded.
Every wave — sound, light, water — obeys v = fλ. Only the speed and the range of values differ between them.
10 Facts About the Wave Equation
The wave equation is v = fλ.
Frequency is measured in hertz (Hz) — cycles per second.
In the same medium the speed is fixed; f and λ are inversely related.
Light travels at ≈ 3 × 10⁸ m/s in a vacuum.
Sound travels at ≈ 343 m/s in air (20 °C).
Wavelength is the distance between two successive crests.
A high frequency means a short wavelength.
The period T is 1/f — the time for one cycle.
Radio, microwave and light are all EM waves.
This calculator runs in your browser — your working stays private.
Frequently Asked Questions
- v = fλ — wave speed equals frequency times wavelength. Rearranged, f = v / λ and λ = v / f. The calculator solves for whichever value you leave blank and shows the answer in SI units: metres per second, hertz and metres.
- SI units: metres per second (m/s) for speed, hertz (Hz) for frequency, metres (m) for wavelength. You may enter kHz or MHz for frequency, and cm, mm or km for wavelength; the tool converts to SI first. Speed and wavelength also show a dimmed US/imperial readout.
- Because the wave speed in a given medium is fixed. From v = fλ, if v stays constant and f increases, then λ must decrease so the product stays the same. This is why high-pitched notes have a shorter wavelength than low-pitched ones.
- Yes. Enter two of speed, frequency and wavelength and leave the third blank — the calculator rearranges v = fλ and solves for the missing value.
- Yes. v = fλ holds for all kinds of waves — sound, light, water and seismic waves. What differs is the wave speed in a given medium, for example about 343 m/s for sound in air and about 3 × 10⁸ m/s for light in a vacuum.
- The physics — v = fλ in SI units — is identical worldwide. What changes is the terminology; "wavelength" is 波长 in Chinese, while SPM students see the Malay term. The calculated value is the same.
- The Tool Information block lists the exact syllabus for your selected curriculum (e.g. SPM Fizik 4531). It is a study aid, not a substitute for your official syllabus or teacher.
- No. Every calculation runs in your browser; nothing you type is uploaded. It works offline once the page has loaded.
- Completely free, no account or usage limit. It runs entirely in your browser and collects no data.
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Method & sources
How it computes
v = f lambda. For light in vacuum the speed is not measured but DEFINED: c = 299 792 458 m/s exactly, since the 17th CGPM redefined the metre in terms of it in 1983. Measuring the speed of light now measures the length of your metre.
What this tool implements
- c is exact by definition in vacuum. In any medium the phase velocity is c/n and is lower; the tool does not silently apply the vacuum value to glass or water.
- The speed of sound is not a constant: about 343 m/s in air at 20 C, rising with temperature, and it depends on the medium far more than on frequency.
- Frequency, wavelength and speed are related for a travelling wave; for a standing wave the boundary conditions decide the permitted wavelengths and this relation alone does not.
Sources
- 17th General Conference on Weights and Measures (CGPM), 1983, Resolution 1 — the definition of the metre fixing c exactly: https://www.bipm.org/en/committees/cg/cgpm/17-1983/resolution-1
- BIPM, The International System of Units (SI Brochure), 9th edition 2019: https://www.bipm.org/en/publications/si-brochure
What can make this go out of date
- None at runtime.
Pick up where you left off
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