Decibel Calculator
Enter a measured power and a reference power to get the ratio expressed in decibels — and see why every 10 dB means ten times the power.
Any power ratio in decibels
Enter the measured power P₁ and the reference power P₂ and the calculator returns the ratio expressed in decibels via dB = 10 × log₁₀(P₁/P₂).
Powers, not voltages
This is the power-ratio formula (factor 10). Voltages or sound pressures use a factor of 20 because power scales with their square.
What is a decibel?
A logarithmic power ratio
A decibel calculator turns the ratio of two powers into a single, compact number on a logarithmic scale. A decibel (dB) is not an absolute amount — it always compares a measured power P₁ against a reference power P₂. Because the scale is logarithmic, it folds an enormous span of values into easy-to-read figures: a ratio of one million to one is just 60 dB. Engineers reach for decibels in acoustics, audio, radio, and signal processing precisely because gains and losses then add and subtract instead of multiplying.
Enter a measured power and a reference power in watts to get the ratio in decibels instantly.
The decibel value is ten times the base-10 logarithm of the power ratio P₁ divided by P₂.
dB = 10 × log₁₀(P₁ / P₂)First divide the measured power by the reference to get the ratio, then take its base-10 logarithm and multiply by ten. A ratio of 1 gives 0 dB, ratios above 1 give positive values, and ratios below 1 give negative values. The logarithm is why such a wide range of powers collapses into a handful of decibels.
Suppose an amplifier outputs 100 W while the reference level is 1 W.
Form the power ratio
100 / 1 = 100 — the measured power is 100 times the reference.
Take the base-10 logarithm
log₁₀(100) = 2 — the exponent that turns 10 into 100.
Multiply by ten
10 × 2 = 20 dB — the gain of the amplifier expressed in decibels.
The decibel figure is best read in steps rather than as a raw count. Each +10 dB corresponds to ten times the power, so 10 dB is a 10× ratio, 20 dB is 100×, and 30 dB is 1000×. Each +3 dB is approximately a doubling of power, because 10 × log₁₀(2) ≈ 3.01 dB — so +6 dB is roughly four times the power and +9 dB about eight times. The pattern works downward too: −3 dB is about half the power and −10 dB is one tenth. A result of 0 dB means the two powers are equal. This additive behaviour is the whole point of the decibel: a +6 dB amplifier feeding a −2 dB cable nets out to +4 dB, no multiplication required. When you read your answer, translate it back into a ratio using these landmarks rather than treating the number as if it were linear.
The formula is exact, but a couple of practical points are worth keeping in mind.
Power ratios only, and both values must be positive
This calculator uses the power-ratio definition with a factor of 10. Field quantities such as voltage, current, or sound pressure use a factor of 20 instead, because power is proportional to their square — do not mix the two. Both inputs must be strictly positive: the logarithm of zero or a negative number is undefined, and a zero reference would divide by zero, so the calculator returns no result in those cases.