Wavelength to frequency calculator
Free-space and on-board wavelength for a frequency, or the frequency for a wavelength, with quarter-wave and half-wave lengths and delay per unit length.
- Wavelength on the board λg (εeff 4)
- 61.18 mm
- Quarter wave on the board λg/4
- 15.3 mm
- Half wave on the board λg/2
- 30.59 mm
- Velocity factor 1/sqrt(εeff)
- 0.5
- Propagation delay
- 6.671 ps/mm
| Medium | λ (mm) | λ/2 (mm) | λ/4 (mm) | λ/4 (in) |
|---|---|---|---|---|
| Free space | 122.4 | 61.18 | 30.59 | 1.204 |
| Board, εeff 4 | 61.18 | 30.59 | 15.3 | 0.6022 |
How this is calculated
λ0 = c / f λg = c / ( f · sqrt(εeff) ) Velocity factor = 1 / sqrt(εeff) Delay per length = sqrt(εeff) / c c = 299 792 458 m/s (exact)
- εeff
- For stripline, fully inside the laminate, εeff is the laminate εr. For microstrip, part of the field is in air, so εeff falls between 1 and εr and depends on trace width and height. Take it from your stackup or impedance calculation.
- Frequency
- Laminate εr varies with frequency. Use the value your fabricator quotes at the frequency of interest.
- BIPM, The International System of Units (SI Brochure), definition of the meter9th edition, 2019, updated 2026
- Texas Instruments SCAA082A, High-Speed Layout Guidelines, Table 1 (wavelength at εeff), section 1.3.1 and Table 2 (stripline εr, microstrip εeff)November 2006, revised August 2017
Questions
At 2.45 GHz, 122.4 mm in free space, so a quarter wave is 30.6 mm. On a board with εeff of 4 the wavelength halves to 61.2 mm and the quarter wave is 15.3 mm.
Signals travel at c / sqrt(εeff) in the dielectric. With εeff of 4 they move at half the speed of light, so each cycle covers half the distance.
Use εr for stripline, which is buried in the laminate. Use εeff for microstrip: it is lower than εr because part of the field is in air, so microstrip is faster than stripline on the same board.
sqrt(εeff) / c. In free space that is 84.7 ps per inch (3.34 ps per mm); with εeff of 4 it doubles to 169.5 ps per inch.