dB (Power)
dB = 10 × log₁₀(P2/P1)
Quick answer
This calculator solves dB = 10 × log₁₀(P2 / P1) for Gain. With Reference Power 10 W, Measured Power 22 W, the result is 3.424 dB. It solves in 3 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The decibel is a logarithmic unit for expressing the ratio between two power levels. It was originally developed by Bell Telephone Laboratories to quantify signal loss in telephone cables. The logarithmic scale is used because human perception of loudness and signal strength is approximately logarithmic, and because it converts multiplication and division of gains into simple addition and subtraction. A gain of +3dB means the power has doubled, +10dB means a tenfold increase, and -3dB means the power has halved. Cascaded amplifier stages can be analyzed by simply adding their individual dB gains.
Variables
- dB — Power ratio in decibels
- P1 — Reference power in watts (W)
- P2 — Measured power in watts (W)
Practical Notes
Key landmarks: 0dB = no change, +3dB = 2x power, +10dB = 10x power, +20dB = 100x power, +30dB = 1000x power. Negative values indicate attenuation. Both P1 and P2 must be positive for the logarithm to be defined.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| dB | Gain | dB | dB |
| P1 | Reference Power | W | µW, mW, W, kW |
| P2 | Measured Power | W | µW, mW, W, kW |
Step by step
- 1. What you know: Reference Power 10 W, Measured Power 22 W
- 2. The relation: dB = 10 × log₁₀(P2 / P1)
- 3. Substitute: P1 = 10 W, P2 = 22 W
- 4. Result: Gain = 3.424 dB
Worked examples
Minimum range
Given: Reference Power 10 mW, Measured Power 22 mW
Result: Gain = 3.424 dB
Low range
Given: Reference Power 100 mW, Measured Power 0.22 W
Result: Gain = 3.424 dB
Typical
Given: Reference Power 10 W, Measured Power 22 W
Result: Gain = 3.424 dB
High range
Given: Reference Power 1 kW, Measured Power 2.2 kW
Result: Gain = 3.424 dB
Maximum range
Given: Reference Power 10 kW, Measured Power 22 kW
Result: Gain = 3.424 dB
Solving for each variable
Solve for Gain
Reference Power 10 mW, Measured Power 22 mW → 3.424 dB
Solve for Reference Power
Gain 0.3 dB, Measured Power 22 mW → 20.53 mW
Solve for Measured Power
Gain 0.3 dB, Reference Power 10 mW → 10.72 mW
How Gain changes with Reference Power
| Reference Power (input) | Gain (result) |
|---|---|
| 1 W | 13.42 dB |
| 2.5 W | 9.445 dB |
| 5 W | 6.435 dB |
| 7.5 W | 4.674 dB |
| 10 W | 3.424 dB |
| 15 W | 1.663 dB |
| 20 W | 0.4139 dB |
| 40 W | -2.596 dB |
| 70 W | -5.027 dB |
| 100 W | -6.576 dB |
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<p><a href="https://vbatpower.com/formulas/db-power/">dB (Power)</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate dB (Power)?
Use dB = 10 × log₁₀(P2 / P1). With Reference Power 10 W, Measured Power 22 W, Gain works out to 3.424 dB.
What is the formula for dB (Power)?
The formula is dB = 10 × log₁₀(P2 / P1). The decibel is a logarithmic unit for expressing the ratio between two power levels.
How do you find Reference Power when you know the other values?
Rearrange for Reference Power: with Gain 0.3 dB, Measured Power 22 mW, Reference Power is 20.53 mW.
How do you find Measured Power when you know the other values?
Rearrange for Measured Power: with Gain 0.3 dB, Reference Power 10 mW, Measured Power is 10.72 mW.
Related Concepts
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