🔊Decibel Calculator
Convert between decibels and a power or amplitude ratio — enter either value.
Free Decibel Calculator
This decibel calculator converts between a decibel value and the underlying ratio it represents, in either direction. For power or intensity ratios (like sound intensity or electrical power), dB = 10·log₁₀(ratio). For amplitude or pressure ratios (like sound pressure or voltage), dB = 20·log₁₀(ratio) — the factor of 20 accounts for power being proportional to amplitude squared.
Leave either the dB or ratio field blank to solve for it. Every 10 dB (power) or 20 dB (amplitude) represents a 10× change in the ratio — a useful mental shortcut for working with the logarithmic decibel scale.
Free, runs entirely in your browser, no sign-up required.
About the Decibel Calculator
Features
Power and amplitude modes
Correct formula for either type of quantity.
Solve either direction
dB to ratio, or ratio to dB.
Step-by-step
See the exact formula applied to your numbers.
Instant, private
Runs entirely in your browser. No data is sent anywhere.
Frequently Asked Questions
What is a decibel?
A decibel (dB) is a logarithmic unit used to express the ratio between two values of power, intensity, or amplitude — it compresses very large ranges of ratios into manageable numbers.
Why are there two formulas — 10·log and 20·log?
Power (and intensity) is proportional to amplitude squared, so converting an amplitude ratio to an equivalent power ratio requires squaring it — which becomes multiplying by 2 in the logarithm, turning 10·log into 20·log for amplitude-based quantities.
When do I use the power formula?
Use dB = 10·log₁₀(ratio) when comparing power or intensity quantities, such as sound intensity (W/m²) or electrical power.
When do I use the amplitude formula?
Use dB = 20·log₁₀(ratio) when comparing amplitude or pressure quantities, such as sound pressure level or voltage.
What does 0 dB mean?
0 dB means the ratio is exactly 1 — the two quantities being compared are equal, since log₁₀(1) = 0.
What does a 3 dB increase mean?
A 3 dB increase roughly doubles the power ratio (10^(3/10) ≈ 2), a common rule of thumb in acoustics and electronics.
Can decibels be negative?
Yes — a negative dB value means the ratio is less than 1, i.e., the measured quantity is smaller than the reference.
Why can't the ratio be zero or negative?
Logarithms are undefined for zero or negative numbers, so a valid ratio must always be a positive number.
Can I solve for the ratio if I know the dB value?
Yes — leave the ratio field blank and enter the dB value, and the calculator solves for the ratio using the inverse formula, ratio = 10^(dB/factor).
Is this calculator free to use?
Yes, completely free with no sign-up, and it runs entirely in your browser.