Part of Engineering utility calculators

Engineering Conversion Calculator

Convert the dimensions, units, gain values, power levels, complex values, and prefixes used in electronics and PCB design.

Conversion

Notes

Dimension conversions support mm, mil, inch, and µm. Power-to-voltage conversion uses RMS voltage and requires an explicit reference impedance.

Voltage gain uses 20 log₁₀(|Aᵥ|). Power in dBm uses 10 log₁₀(P/1 mW). Complex conversion uses atan2, preserving sign and quadrant.

When to use it

Use engineering conversions to avoid unit, prefix, and dB mistakes between calculations

Electronics work constantly moves between SI prefixes, PCB dimensions, voltage gain, dB, dBm, RMS voltage, complex values, phase, and temperature. This calculator keeps those conversions close to the design calculators that need them.

Dimensions

Examples: mm, mil, inch, µm

Use for PCB clearances, package dimensions, hole sizes, copper features, and mechanical notes.

Temperature

Examples: °C, °F, K

Use for datasheet limits, lab conditions, environmental specs, and thermal calculations.

Voltage gain and dB

Examples: ratio ↔ dB

Uses 20 log10(|Av|), because this is an amplitude ratio conversion.

Power, dBm, and RMS voltage

Examples: dBm, W, Vrms

Uses RMS voltage and an explicit reference impedance.

Complex and angle

Examples: rectangular, polar, degrees, radians

Useful for impedance, phase, vectors, and transfer-function notes.

SI prefixes

Examples: p, n, µ, m, k, M, G

Use for quick electronics-scale value changes without mental prefix mistakes.

Logarithmic conversions and reference levels

Unit conversions are not all the same. Some are exact scale factors, while dB and dBm depend on logarithmic relationships and reference assumptions.

Gain dB = 20 log10(|Av|)

Voltage gain to dB

Use for amplitude, voltage, and gain ratios.

dBm = 10 log10(P / 1 mW)

Power to dBm

Power in dBm is referenced to 1 mW.

Vrms = √(P × R)

Power to RMS voltage

Requires an explicit impedance because voltage depends on load resistance.

Worked examples

These examples are covered by the engineering conversion test suite.

Unit and prefix conversions

PCB dimension: 10 mil = 0.254 mm.

SI prefix: 4.7 µF = 4700 nF.

Angle: 180° = π radians.

dB, dBm, and RMS voltage

Voltage gain: a gain ratio of 2 is 6.02 dB.

Power level: 0 dBm = 1 mW.

RMS voltage: 1 mW into 50 Ω gives √(0.001 × 50) = 223.6 mV RMS.

Common mistakes to avoid

Most conversion mistakes are not arithmetic errors. They are reference, unit, or interpretation errors.

Amplitude versus power

Use 20 log10 for voltage or amplitude ratios.
Use 10 log10 for power ratios.
Keep dB ratio conversions separate from absolute levels like dBm.

RMS and impedance assumptions

Power-to-voltage conversion uses RMS voltage.
The result changes with reference impedance.
Peak, peak-to-peak, and RMS values are not interchangeable.

Assumptions and limitations

Conversions do not validate design

A converted value can still be unsuitable for a datasheet limit, PCB rule, or signal-chain budget.

Reference levels matter

dBm is referenced to 1 mW. Voltage from power needs the impedance, and the calculator reports RMS voltage.

Sign and quadrant matter

Complex conversion uses quadrant-aware angle handling. Preserve signs when moving between rectangular and polar forms.

Related calculators and next checks

Conversions usually sit between design checks. Follow the calculator that owns the actual engineering decision.

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Engineering utility hub

Follow utility calculators for repeated electronics design conversions.

FAQ

Which conversions are exact?

Pure unit conversions such as inch to mm, degree to radian, SI prefixes, and Celsius/Kelvin offsets are deterministic once the unit definitions are chosen. They do not validate whether the converted value is appropriate for a design.

Why does dBm need a reference impedance for voltage?

dBm is a power level referenced to 1 mW. Converting that power to voltage requires load impedance, and the calculator reports RMS voltage.

Why is voltage gain dB different from power dB?

Voltage gain uses 20 log10 of an amplitude ratio. Power uses 10 log10 of a power ratio. Mixing these is a common source of 2× errors in dB calculations.

Performs exact unit transforms and standard logarithmic engineering conversions without adding arbitrary tolerance controls.

Equations and variables

Voltage gain in dBdB = 20 * log10(|Av|)

Power level in dBmdBm = 10 * log10(P / 1 mW)

RMS voltage from powerVrms = sqrt(P * R)

Av: Voltage gain (V/V)
P: Power (W)
R: Reference impedance (ohm)

Assumptions and limitations

Assumptions

Conversions use exact scale factors or conventional logarithmic relationships.
Temperature conversion inputs must be physically valid.

Limitations

No measurement uncertainty is inferred.
Power and voltage conversions assume RMS quantities and a real reference impedance.

Worked example and design use

Power and gain conversions

Inputs: 20 dB voltage gain, 0 dBm into 50 ohm

Outputs: Av = 10 V/V, P = 1 mW and Vrms about 224 mV

Design guidance

Keep measurement tolerance in the source data rather than adding tolerance controls to exact unit transformations.
Check whether RF and audio contexts use RMS, peak, peak-to-peak, or dB reference conventions.