Wavelength
λ = c / f
Quick answer
This calculator solves λ = c / f for Wavelength. With Frequency 2.4 GHz, the result is 12.49 cm. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The wavelength of an electromagnetic wave is inversely proportional to its frequency, with the speed of light (approximately 3 × 10^8 m/s in vacuum) as the constant of proportionality. This relationship is fundamental to antenna design, where antenna dimensions are typically fractions or multiples of the wavelength. For example, a quarter-wave antenna for 2.4 GHz WiFi is about 3.1 cm long. Wavelength also determines how signals interact with objects: signals with wavelengths much larger than an obstacle diffract around it, while shorter wavelengths are reflected or absorbed.
Variables
- λ — Wavelength in meters (m)
- f — Frequency in hertz (Hz)
- c — Speed of light ≈ 3 × 10⁸ m/s
Practical Notes
In transmission lines and PCB traces, the effective wavelength is shorter than free space due to the dielectric constant: λ_eff = λ / √εr. At 1 GHz, the free-space wavelength is 30 cm. When trace lengths approach λ/10, transmission line effects become significant and impedance matching is required.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| lambda | Wavelength | m | mm, cm, m, km |
| f | Frequency | GHz | Hz, kHz, MHz, GHz |
Step by step
- 1. What you know: Frequency 2.4 GHz
- 2. The relation: λ = c / f
- 3. Substitute: f = 2.4 GHz
- 4. Result: Wavelength = 12.49 cm
Worked examples
Minimum range
Given: Frequency 100 MHz
Result: Wavelength = 2.998 m
Low range
Given: Frequency 1 GHz
Result: Wavelength = 29.98 cm
Typical
Given: Frequency 2.4 GHz
Result: Wavelength = 12.49 cm
High range
Given: Frequency 10 GHz
Result: Wavelength = 2.998 cm
Maximum range
Given: Frequency 100 GHz
Result: Wavelength = 2.998 mm
Solving for each variable
Solve for Wavelength
Frequency 100 MHz → 2.998 m
Solve for Frequency
Wavelength 1 mm → 299.8 GHz
How Wavelength changes with Frequency
| Frequency (input) | Wavelength (result) |
|---|---|
| 0.24 GHz | 1.249 m |
| 0.6 GHz | 49.97 cm |
| 1.2 GHz | 24.98 cm |
| 1.8 GHz | 16.66 cm |
| 2.4 GHz | 12.49 cm |
| 3.6 GHz | 8.328 cm |
| 4.8 GHz | 6.246 cm |
| 9.6 GHz | 3.123 cm |
| 16.8 GHz | 1.784 cm |
| 24 GHz | 12.49 mm |
The same result in other units
| Unit | Value |
|---|---|
| mm | 124.9 |
| cm | 12.49 |
| m | 0.1249 |
| km | 0.0001249 |
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<p><a href="https://vbatpower.com/formulas/wavelength/">Wavelength</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Wavelength?
Use λ = c / f. With Frequency 2.4 GHz, Wavelength works out to 12.49 cm.
What is the formula for Wavelength?
The formula is λ = c / f. The wavelength of an electromagnetic wave is inversely proportional to its frequency, with the speed of light (approximately 3 × 10^8 m/s in vacuum) as the constant of proportionality.
How do you find Frequency when you know the other values?
Rearrange for Frequency: with Wavelength 1 mm, Frequency is 299.8 GHz.
What units does Wavelength use?
Wavelength is shown in mm, cm, m, km. Values are held in SI base units internally, so you can mix prefixes without converting by hand.
Related Concepts
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