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Full changelogEngine 1.18.3

dB, dBm & RMS Converter

Fundamentals

Convert between watts, dBm and RMS or peak-to-peak voltage in a given impedance.

Inputs

50 Ω RF, 75 Ω video, 600 Ω legacy audio
Ω

Results

Power P

Not judged: a unit conversion, so there is nothing to pass or fail.
1mW
RMS voltage Vrms
223.6mV
Peak-to-peak Vpp

peak 316.2 mV
632.5mV
All results (3)
Level

-30.00 dBW
0.00dBm
RMS current Irms
4.472mA
dBV / dBu

ref 1 V / 0.7746 V
-13.01/ -10.79
Common ratios
dBPower ratioVoltage ratio
1 dB1.26×1.12×
3 dB2×1.41×
6 dB4×2×
10 dB10×3.16×
20 dB100×10×
−3 dB0.5×0.707×

Accuracy

Verified against

4 independent cases. See the working.

This is a design aid. The engineer remains responsible for the design and for checking the standard itself.

Parameter sweep

Vary one input over a range and see the answer and verdict at each step, as a table and a curve.Pro

Worst-case corners

Put a tolerance on each input and get the worst-case band around the answer.Pro

The principle

The decibel is a logarithmic ratio. It becomes an absolute level only with a reference: dBm is relative to 1 mW, dBW to 1 W, dBV to 1 V RMS and dBu to 0.7746 V RMS (1 mW in 600 Ω).

Power ratio
LdB=10log⁡10 ⁣P2P1L_{dB} = 10 \log_{10}\!\frac{P_2}{P_1}
Voltage ratio (same impedance)
LdB=20log⁡10 ⁣V2V1L_{dB} = 20 \log_{10}\!\frac{V_2}{V_1}
The 20 comes from P ∝ V², so it holds only when both impedances are equal.
Absolute level
PdBm=10log⁡10 ⁣(P1 mW)P=Vrms2Z0P_{dBm} = 10 \log_{10}\!\left(\frac{P}{1\,\t{mW}}\right) \qquad P = \frac{V_{rms}^{2}}{Z_0}
Sine relations
Vrms=Vpk2=Vpp22V_{rms} = \frac{V_{pk}}{\sqrt{2}} = \frac{V_{pp}}{2\sqrt{2}}
Sine only. Square wave: Vrms = Vpk; triangle: Vpk/√3.
  • PPpower in watts
  • Z0Z_0system impedance
  • VrmsV_{rms}RMS voltage across Z₀
More detail

Common traps

  • dBm is power. 0 dBm is 1 mW in any impedance, but it is 224 mV RMS in 50 Ω and 274 mV in 75 Ω.
  • dB add as gains. A +12 dB amplifier then a −3 dB cable gives +9 dB. Two equal uncorrelated signals sum to +3 dB; two equal in-phase signals to +6 dB.
  • RMS sets the heating. Power in a resistor is Vrms²/R for any waveform, so use a true-RMS meter on PWM and switching nodes.
Mental arithmetic. +3 dB ≈ ×2 power, +10 dB = ×10, so +13 dB ≈ ×20 and +20 dB = ×100. Build any number from 3s and 10s.
Reference: IEC 60027-3 (logarithmic quantities and units).

Engine version ⁨1.18.3⁩