Decibel Calculator (dB, dBm, dBV, dBu)
Every decibel conversion an RF, audio or test engineer needs, with the working.
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About the Decibel Calculator (dB, dBm, dBV, dBu)
Four calculators for decibels in one place. dBm, watts and volts converts a level in dBm, dBW, dBµW, watts, dBV, dBu, dBmV, dBµV or volts (rms, peak or peak-to-peak) into all of the others at 50 Ω, 75 Ω, 600 Ω or any impedance. Ratio ↔ dB turns power and voltage ratios into decibels and back, with nepers. Add levels adds unrelated sources (noise, machines, carriers) as powers, takes a background level away from a total, or averages levels on energy. VSWR and return loss converts between VSWR, return loss, the reflection coefficient and mismatch loss, or works them out from a load impedance.
Every result shows its formula and numbers, and the tables list the level in every unit or the VSWR figures around yours.
Without a pass, the free preview runs on your own values: it shows the notes that apply and the labels of the first rows of each table, with the converted level, ratio, total or match, every other figure and the working hidden; the full result, Copy result and the CSV come with a Pro pass.
How to use it
- Choose what to work out: dBm, watts & volts, Ratio ↔ dB, Add levels or VSWR & return loss.
- Type the value and pick its unit. For levels, choose the impedance (50 Ω for RF, 75 Ω for video and cable TV, 600 Ω for older audio lines) and the unit to show the answer in.
- To add levels, type them one per line; to take one away, put the total first. For a match, type the VSWR, return loss, |Γ| or mismatch loss, or the load’s R and X.
- Read the result, the table and the working, then copy the result or download it as CSV — with a pass, or after unlocking this result.
Examples
0 dBm, 50 Ω
1 mW = 223.6 mV rms = −13.01 dBV = 106.99 dBµV
30 dBm, 50 Ω
7.071 V rms, 10 V peak, 20 V peak-to-peak
+4 dBu
1.228 V rms (0 dBu = 0.7746 V, the voltage that puts 1 mW into 600 Ω)
0 dBmV at 75 Ω
−48.75 dBm = 60 dBµV
90 dB + 90 dB
93.01 dB, not 180 dB
87 dB with the machine running, 83 dB background
The machine alone: 84.8 dB
VSWR 1.5
Return loss 13.98 dB, |Γ| = 0.2, 4 % of the power reflected, mismatch loss 0.177 dB
Power and voltage decibels
- Power ratio: L = 10·log₁₀(P₂/P₁) dB, and P₂/P₁ = 10^(L/10). Doubling the power is +3.01 dB.
- Voltage or current ratio: L = 20·log₁₀(V₂/V₁) dB, and V₂/V₁ = 10^(L/20). Doubling the voltage is +6.02 dB. The two give the same number only across the same impedance, because P = V²/R.
- Nepers: 1 Np = 20/ln 10 ≈ 8.686 dB; a level in nepers is ln(V₂/V₁), or ½·ln(P₂/P₁).
These are the definitions of IEC 60027-3, Letter symbols to be used in electrical technology — Part 3: Logarithmic and related quantities, and their units; for telecommunications, Recommendation ITU-R V.574 (Use of the decibel and the neper in telecommunications) covers the same units.
Absolute levels and their references
- dBm is power relative to 1 mW, dBW to 1 W (0 dBW = 30 dBm) and dBµW to 1 µW.
- dBV is voltage relative to 1 V rms, dBmV to 1 mV and dBµV to 1 µV, whatever the impedance.
- dBu is relative to 0.7746 V rms (√0.6 V), the voltage that dissipates 1 mW in 600 Ω, so at 600 Ω dBu and dBm are the same number; 0 dBu is −2.218 dBV.
- Converting between a power unit and a voltage unit needs the impedance: V = √(P·R). Peak and peak-to-peak values assume a sine wave (V_peak = √2·V_rms).
Adding decibels
Unrelated sources add as powers: L = 10·log₁₀(10^(L₁/10) + 10^(L₂/10) + …). Two equal levels give +3.01 dB; a level 10 dB below another adds only 0.41 dB. Taking a background away works the same way with a minus sign, and needs the total to be clearly above the background: within 3 dB the result is very sensitive to small errors. The energy average is 10·log₁₀ of the mean power, which is always at least the arithmetic mean of the levels. Coherent signals (two copies of one signal in phase) add as voltages instead and are not covered here.
VSWR, return loss and mismatch loss
- Reflection coefficient: Γ = (Z_L − Z₀) ÷ (Z_L + Z₀); for a measurement, |Γ| = (VSWR − 1) ÷ (VSWR + 1).
- VSWR = (1 + |Γ|) ÷ (1 − |Γ|), from 1 (matched) to infinity (open, short or pure reactance).
- Return loss: RL = −20·log₁₀|Γ| dB, a positive number; a network analyser’s S11 is the same figure with a minus sign.
- Mismatch loss: ML = −10·log₁₀(1 − |Γ|²) dB, the power that does not reach the load because it is reflected. The reflected share of the power is |Γ|².
These are the relations of transmission-line theory, as in Pozar’s Microwave Engineering.
Limitations
- Peak and peak-to-peak conversions assume a sine wave; other waveforms have other crest factors.
- Adding levels assumes unrelated (incoherent) sources. Signals that are correlated or in phase add differently.
- Mismatch loss counts only the reflection at the load; cable loss and a mismatched source are separate.
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Frequently asked questions
What do I get without a pass?
Without a pass, Decibel Calculator (dB, dBm, dBV, dBu) shows the names of each table’s first rows (up to 3), with the converted level, ratio, total or match, the working and every other figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I convert dBm to watts?
P = 1 mW × 10^(dBm/10). 0 dBm is 1 mW, 10 dBm is 10 mW, 20 dBm is 100 mW and 30 dBm is 1 W; −30 dBm is 1 µW. The other way round, dBm = 10·log₁₀(P ÷ 1 mW).
How do I convert dBm to volts?
You need the impedance: V_rms = √(P × R). At 50 Ω, 0 dBm (1 mW) is √(0.001 × 50) = 0.2236 V rms; at 75 Ω it is 0.2739 V; at 600 Ω it is 0.7746 V, which is why 0 dBm and 0 dBu coincide at 600 Ω.
What is the difference between dBu and dBV?
Only the reference: dBV is relative to 1 V rms and dBu to 0.7746 V rms. A level in dBu is 2.218 dB higher than the same voltage in dBV, so the +4 dBu professional level is 1.228 V and the −10 dBV consumer level is 0.316 V.
Why do two 90 dB sources make 93 dB and not 180 dB?
Decibels are logarithmic: doubling the power adds 10·log₁₀ 2 = 3.01 dB. To add levels, turn each into a power, add the powers and take the logarithm again; the calculator does this for any number of levels.
What return loss is a VSWR of 2:1?
|Γ| = (2 − 1) ÷ (2 + 1) = 1/3, so the return loss is −20·log₁₀(1/3) = 9.54 dB and 11.1 % of the power is reflected; the mismatch loss is 0.51 dB. A 1.5:1 VSWR is 13.98 dB of return loss.