# Electromagnetic Wave Calculator (c = λf)

Calculate EM wave properties: convert between frequency and wavelength (c = lambda f), find photon energy (E = hf), and identify the spectrum band from radio to gamma.

## What this calculates

All electromagnetic waves travel at the speed of light (about 300 million m/s in vacuum), but they span a huge range of frequencies and wavelengths. Your WiFi router broadcasts at 2.4 GHz (12.5 cm wavelength), while visible red light oscillates at 430 trillion Hz (700 nm). This calculator converts between frequency and wavelength, finds photon energy, and identifies where a wave sits on the EM spectrum.

## Inputs

- **Calculate From** — options: Frequency to Wavelength, Wavelength to Frequency
- **Frequency** (Hz) — min 0 — Used when calculating from frequency
- **Wavelength** (m) — min 0 — Used when calculating from wavelength

## Outputs

- **Frequency** (Hz) — Electromagnetic wave frequency
- **Wavelength** (m) — Electromagnetic wave wavelength
- **Photon Energy** (J) — Energy of one photon (E = hf)
- **Photon Energy** (eV) — Photon energy in electron volts
- **EM Spectrum Band** — formatted as text — Which part of the electromagnetic spectrum

## Details

## Core Formulas

### Speed of Light Relation
**c = lambda x f**

The speed of light (c = 2.998 x 10 to the 8 m/s) is a constant. Increase frequency, and wavelength shrinks proportionally.

### Photon Energy
**E = hf = hc / lambda**

Planck's constant h = 6.626 x 10 to the negative 34 J s. Higher frequency (shorter wavelength) means more energy per photon. This is why UV light causes sunburn but radio waves do not.

### The Electromagnetic Spectrum

| Band | Frequency Range | Wavelength | Everyday Example |
|------|----------------|------------|-----------------|
| Radio | 3 kHz - 300 MHz | 1 km - 1 m | AM/FM radio |
| UHF | 300 MHz - 3 GHz | 1 m - 10 cm | TV, cell phones |
| Microwave | 3 GHz - 300 GHz | 10 cm - 1 mm | WiFi, microwave ovens |
| Infrared | 300 GHz - 430 THz | 1 mm - 700 nm | TV remotes, heat |
| Visible | 430 - 750 THz | 700 - 400 nm | Human vision |
| Ultraviolet | 750 THz - 30 PHz | 400 nm - 10 nm | Sunburn, sterilization |
| X-ray | 30 PHz - 30 EHz | 10 nm - 10 pm | Medical imaging |
| Gamma | > 30 EHz | < 10 pm | Nuclear reactions |

### Common Frequencies

- **AM radio:** 540-1600 kHz (wavelengths of 187-556 m)
- **FM radio:** 88-108 MHz (2.8-3.4 m)
- **WiFi 2.4 GHz:** 12.5 cm wavelength
- **WiFi 5 GHz:** 6 cm wavelength
- **5G mmWave:** 24-39 GHz (7.7-12.5 mm)
- **Microwave oven:** 2.45 GHz (same band as WiFi)

## Frequently Asked Questions

**Q: Why do all EM waves travel at the same speed?**

A: In vacuum, the speed of electromagnetic waves is determined by the electric and magnetic properties of space itself (the permittivity and permeability of free space). Maxwell's equations give c = 1 / sqrt(epsilon0 x mu0), which works out to about 3 x 10 to the 8 m/s regardless of frequency. In materials like glass or water, different frequencies travel at slightly different speeds (dispersion), which is what creates rainbows.

**Q: What is the difference between frequency and wavelength?**

A: Frequency is how many wave cycles pass a point per second (measured in Hz). Wavelength is the physical distance between two identical points on consecutive waves (measured in meters). They are inversely related: double the frequency and the wavelength halves. For EM waves, their product always equals the speed of light.

**Q: Why does photon energy matter?**

A: Photon energy determines how EM radiation interacts with matter. Low-energy radio photons (10 to the negative 7 eV) pass harmlessly through your body. Visible light photons (1.8-3.1 eV) trigger chemical reactions in your retina. UV photons (3-124 eV) break molecular bonds in DNA, causing sunburn. X-ray photons (100+ eV) penetrate tissue but are absorbed by bone, enabling medical imaging.

**Q: Why does a microwave oven use the same frequency as WiFi?**

A: Both operate near 2.45 GHz, which is in the ISM (Industrial, Scientific, Medical) band -- a range reserved for non-communication uses. The microwave oven was invented first, and the band was later opened for low-power devices like WiFi routers. Water molecules absorb 2.45 GHz energy particularly well, which is why microwaves heat food. WiFi signals are thousands of times weaker and do not cause heating.

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Source: https://vastcalc.com/calculators/physics/electromagnetic-wave
Category: Physics
Last updated: 2026-04-08