Decibel Calculator (Power Ratio)
Converts a ratio of two power levels into decibels using 10 × log10(P1 ÷ P2). Decibels express how many times larger or smaller one power is than another on a logarithmic scale used in acoustics, electronics, and signal processing.
Last updated: May 2026
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About this calculator
The decibel (dB) is a logarithmic unit for comparing two power levels, defined as dB = 10 × log10(P1 ÷ P2). Because it is logarithmic, it compresses huge ranges into manageable numbers and turns multiplication into addition — two stages of gain add in decibels rather than multiply. A power ratio of 2 is about +3 dB, a ratio of 10 is exactly +10 dB, and a ratio of 100 is +20 dB; ratios below 1 give negative decibels (a loss). For example, 100 W compared with a 1 W reference is 10 × log10(100) = 10 × 2 = 20 dB. The key thing to remember is that this formula is for power ratios. When you are working with amplitude quantities — voltage, current, sound pressure — the relationship to power is squared, so the correct formula becomes 20 × log10(amplitude ratio); using the 10× power formula on a voltage ratio gives an answer that is half what it should be. Decibels are also often quoted relative to a fixed reference, written with a suffix: dBm uses 1 milliwatt as the reference, dBW uses 1 watt, and dB SPL uses the threshold of human hearing as the sound-pressure reference. This calculator gives a plain power ratio in dB; choose your two power values consistently. Decibels are everywhere in engineering because human perception of sound and light is roughly logarithmic, and because signal gains and losses through cables, amplifiers, and filters chain together by simple addition once expressed in dB.
How to use
Example 1 — Amplifier gain. An amplifier outputs 100 W from a 1 W input. Enter 100 and 1. Result: 20 dB. Verify: 100 ÷ 1 = 100; log10(100) = 2; 10 × 2 = 20 dB. ✓ A tenfold power increase is +10 dB, so a hundredfold is +20 dB. Example 2 — Cable loss. A signal enters a cable at 50 W and leaves at 25 W. Enter 25 and 50. Result: about −3.01 dB. Verify: 25 ÷ 50 = 0.5; log10(0.5) ≈ −0.301; 10 × −0.301 ≈ −3.01 dB. ✓ Halving the power is the classic "−3 dB" point.
Frequently asked questions
When do I use 10·log versus 20·log?
Use 10·log10 when you are comparing power (watts) — that is what this calculator does. Use 20·log10 when you are comparing amplitude quantities such as voltage, current, or sound pressure, because power is proportional to the square of amplitude, and the squaring brings a factor of 2 out of the logarithm. For example, doubling voltage is +6 dB, while doubling power is +3 dB. A very common mistake is applying the 10× power formula to a voltage ratio, which halves the true decibel figure. Decide first whether your quantities are power or amplitude, then pick the matching formula.
Why is doubling power only +3 dB?
Because the scale is logarithmic. A ratio of 2 has a base-10 logarithm of about 0.301, and 10 × 0.301 ≈ 3.01, so doubling power adds roughly 3 dB rather than "doubling" the decibel value. This is one of the most useful rules of thumb in engineering: +3 dB means twice the power, −3 dB means half, +10 dB means ten times, and −10 dB means one tenth. The logarithmic nature is also why decibels can be added: chaining a +10 dB amplifier and a +3 dB stage gives +13 dB total, equivalent to multiplying the power ratios (10 × 2 = 20). This additive convenience is the main reason decibels are used.
What is the difference between dB, dBm, and dB SPL?
A plain decibel (dB) is a relative ratio between two quantities you provide — it has no fixed reference. dBm, dBW, and dB SPL are absolute units that fix the reference: dBm is power relative to 1 milliwatt, dBW is relative to 1 watt, and dB SPL is sound pressure relative to the threshold of human hearing (20 micropascals). So 0 dBm always means exactly 1 mW, whereas 0 dB just means the two powers are equal. This calculator computes a relative ratio; to express a value in dBm, set the reference power to 0.001 W (1 mW). Mixing up relative dB and absolute dBm is a frequent source of confusion in RF work.
What mistakes do people make with decibel calculations?
The most common is using the wrong formula — applying 10·log to a voltage or sound-pressure ratio when 20·log is required, which halves the result. Another is swapping the measured and reference powers, which flips the sign (gain becomes loss). People also try to take the log of zero or a negative power, which is undefined; both inputs must be positive. Forgetting which reference an absolute unit uses (treating dBm as plain dB) leads to errors of 30 dB in RF calculations. Finally, because the scale is logarithmic, people underestimate how large a "small" dB change is — +20 dB is a hundredfold power increase, not twenty times.
When should I not use this power-ratio formula?
Do not use the 10·log10 power formula when your inputs are amplitudes (voltage, current, or sound pressure) rather than powers — switch to 20·log10 instead. It is also inappropriate when either value is zero or negative, since the logarithm is undefined; decibels only describe positive power ratios. If you need an absolute level in dBm, dBW, or dB SPL, you must use the specific reference for that unit rather than an arbitrary second value. And for perceptual loudness judgments, remember that equal dB changes are not perceived equally across all frequencies — A-weighting and loudness models exist precisely because raw dB SPL does not match human hearing perfectly.