A decibel calculator converts signal power and voltage ratios into decibels, then derives dBm, VSWR, Neper values, and perceived loudness using IEC and ISO logarithmic definitions.
Decibel Calculator: Convert Power and Voltage Ratios to dB
This calculator converts a power or voltage ratio between two signal values into decibels, then maps that value into absolute levels (dBm), Nepers, apparent distance change, perceived loudness, and RF mismatch parameters like VSWR and return loss. RF/microwave engineers, audio and acoustics engineers, and telecom technicians use it to move between linear signal ratios and the logarithmic figures printed on datasheets and test reports.
How to Use the Power-to-Decibel and Voltage-to-Decibel Converter
Select whether you’re comparing power values (watts) or voltage values (volts), then enter a Reference Value ($P_1$) and Measured Value ($P_2$) and calculate. The output shows the Decibel Ratio, equivalent absolute levels in dBm, the matching ratio in the other domain, Neper and distance/loudness mappings, and RF mismatch values (VSWR, reflected power, mismatch loss).
The Decibel Formula: 10 log₁₀ for Power, 20 log₁₀ for Voltage
For a power ratio:
$$dB = 10 \log_{10}\left(\frac{P_2}{P_1}\right)$$
For a voltage, current, or sound-pressure ratio — quantities where power is proportional to the square of the value — the multiplier becomes 20:
$$dB = 20 \log_{10}\left(\frac{V_2}{V_1}\right)$$
Both forms come from the same decibel definition set out in IEC 60027-3 and ISO 80000-3, and repeated in ITU-R Recommendation V.574-5. $P_1$ or $V_1$ is the reference you’re comparing against; $P_2$ or $V_2$ is the signal you’re evaluating.
Three input mistakes that throw off the result:
- Using the 10-log formula on a voltage or sound-pressure ratio instead of 20-log — this halves the dB figure you should get.
- Comparing two voltage or current readings taken across different impedances. Per ITU-R V.574-5, a voltage-ratio dB value is only valid when both quantities are measured across equal impedances.
- Treating a difference between two absolute levels (like 40 dBm and 30 dBm) as if it were itself an absolute value — the correct read is a 10 dB relative difference, not “10 dBm.”
Extended Outputs: Nepers, RF Mismatch, and Perceived Loudness
A Neper is the natural-log counterpart to the decibel. Per ITU-R Recommendation V.574-5, $1 \text{ Np} \approx 8.686 \text{ dB}$, so dividing your dB result by 8.686 gives the Neper equivalent.
The Network Mismatch panel treats the magnitude of your dB value as a return loss and back-calculates the reflection coefficient using the standard RF relationships $RL(dB) = -20\log_{10}|\Gamma|$ and $VSWR = \frac{1+|\Gamma|}{1-|\Gamma|}$, per Keysight’s published return-loss and VSWR formulas.
This only produces a meaningful VSWR or mismatch-loss reading if the dB value actually represents a signal reflected from an impedance discontinuity — running an arbitrary gain or attenuation figure through this panel still returns a number, but it won’t correspond to a real standing-wave ratio.
The Acoustic Loudness output doesn’t scale with the raw power ratio. Per the Merck Manual, human hearing perceives a 10 dB increase as roughly a doubling of loudness, even though it’s a tenfold increase in actual sound intensity — so the loudness multiplier moves in powers of two per 10 dB rather than in powers of ten.
The Decibel Scale: How Common Ratios Map to dB
Common Power and Voltage Ratios at Standard dB Values
| dB | Power Ratio (P₂/P₁) | Voltage Ratio (V₂/V₁) |
|---|---|---|
| -20 | 0.01 | 0.10 |
| -10 | 0.10 | 0.32 |
| -6 | 0.25 | 0.50 |
| -3 | 0.50 | 0.71 |
| 0 | 1.00 | 1.00 |
| 3 | 2.00 | 1.41 |
| 6 | 3.98 | 2.00 |
| 10 | 10.00 | 3.16 |
| 20 | 100.00 | 10.00 |
Common Questions About Converting Signals to Decibels
What is a decibel (dB)?
The decibel is a logarithmic unit expressing the ratio between two power or field-quantity values. Per IEC 60027-3 and ISO 80000-3, it’s defined as one-tenth of a bel, applied as $10\log_{10}(P_2/P_1)$ for power ratios.
Why is voltage multiplied by 20 log₁₀ instead of 10 log₁₀?
Because power is proportional to the square of voltage or current, squaring the ratio inside the logarithm is equivalent to doubling the multiplier — per IEC 60027-3 and ISO 80000-3, that’s why the coefficient becomes 20 instead of 10.
What does a negative dB value mean?
A negative dB value means the measured value is smaller than the reference — it’s a loss or attenuation, not a gain. For example, -10 dB means the measured power is one-tenth of the reference power.
How is a Neper related to a decibel?
Per ITU-R Recommendation V.574-5, 1 Neper equals approximately 8.686 dB. Both are logarithmic ratio units — the neper uses the natural logarithm (base e), while the decibel uses the base-10 logarithm.
Does doubling the power double the perceived loudness?
No. Per the Merck Manual, human hearing perceives roughly a doubling of loudness for each 10 dB increase, even though a 10 dB increase corresponds to a tenfold increase in actual sound power or intensity.