Decibel (Power Ratio)
Express a power ratio in decibels.
Formula
Variables
Example
P_2 = 100×P_1: L = 20 dB
How it works
This formula converts a ratio of two powers into the logarithmic decibel scale, which is useful because power changes in signals often span huge ranges. The factor of 10 appears because decibels are defined as ten times the base-10 logarithm of a power ratio, so equal multiplicative changes in power become additive changes in dB. A positive result means the measured power is larger than the reference power, while a negative result means it is smaller.
When to use it
Use this when comparing two power quantities in audio, communications, electronics, or acoustics, such as signal strength, transmitter output, or noise power. It is especially helpful when you want to express large ratios in a compact form.
Worked example, step by step
Suppose a signal has power P1 = 2 mW and another has power P2 = 8 mW. L = 10 log10(P2 / P1) L = 10 log10(8 / 2) L = 10 log10(4) L = 10 × 0.602 L = 6.02 dB So the measured power is 6.02 dB above the reference power.
Common mistakes to avoid
- Using 20 log10 instead of 10 log10 for a power ratio
- Reversing P1 and P2, which flips the sign of the result
- Forgetting that the logarithm needs a pure ratio, not two separate power values with units
Did You Know?
Decibels turn the vast range of real-world power levels into a compact, addable scale.
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