Frequency to wavelength calculator

Wavelength formula: frequency to wavelength and back

Wavelength is the distance covered in one cycle, so the wavelength equation has two inputs: the frequency and how fast the wave moves in the medium.

The velocity depends on the medium:

The last two describe the same effect, so either number can be found from the other:

These assume a non-magnetic material (relative permeability of 1), the normal case for PCB laminates and cable insulation. As a check, TI’s AN-905 reads 56 ps/cm (142 ps/in) for a stripline with εr = 2.8, and √2.8 ÷ c works out to 55.82 ps/cm (141.8 ps/in).

How to calculate wavelength from frequency: worked examples

Frequency to wavelength table, MHz to GHz

Free space, Belden 8259 RG-58A/U at 66 % velocity, and a dielectric of εr = 3.66. Lower-frequency rows in εr 3.66 are arithmetic only: Rogers rates that design value from 8 to 40 GHz. Cable rows above 1 GHz are arithmetic too: Belden’s attenuation table stops at 1 GHz.

Velocity and delay by medium

Data sheet values where a product is named. The plain εr rows are round numbers for comparison, so use your own laminate’s value for a real design.

Getting the velocity right

The medium is where the error comes from, not the arithmetic. Cable sold under one RG number can differ: Belden lists 66 % for solid polyethylene RG-58A/U and 73 % and 75 % for foam types, so a stub cut from the wrong assumption will be off by more than 10 %. Check the data sheet for the exact part.

Laminate values depend on how they were measured. Rogers quotes RO4350B at 3.48 ± 0.05 as a process value (clamped stripline at 10 GHz) and 3.66 as a design value (differential phase length, 8 to 40 GHz), and describes the design value as an average across tested lots. For electrical length the phase-based number is the natural choice. For microstrip the field is partly in air, so enter the effective dielectric constant rather than the laminate number.

Glossary

Wavelength (λ)

The distance a wave travels during one cycle.

Velocity factor (VF)

Propagation speed in a line as a fraction of the speed of light.

Dielectric constant (εr or Dk)

The permittivity of a material relative to vacuum.

Effective dielectric constant

The single value that gives the same speed as a line whose field is partly in air, such as microstrip.

Electrical length

A physical length expressed as a fraction of a wavelength or in degrees, where one wavelength is 360°.

Propagation delay

The time a signal takes to travel a given distance, equal to 1 ÷ v.

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Frequently asked questions

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Sources

• NIST CODATA: speed of light in vacuum (exact)
• Texas Instruments AN058 (SWRA161B), Equation 1 and Table 1 of wavelengths
• Texas Instruments AN-905 (SNLA035), Transmission Line RAPIDESIGNER guide: stripline intrinsic delay at a given εr
• Belden 8259 RG-58A/U data sheet (mirror copy): 66 % nominal velocity, 1.54 ns/ft; its catalog page lists foam 8219 at 73 % and 9311 at 75 %
• Rogers RO4000 laminates data sheet: process and design dielectric constants