Decibel Calculator
The ratio machine: two levels in, a decibel difference out — the power road (10·log) and the amplitude road (20·log) side by side, with the never-add rule priced in your own numbers.
Decibel Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Ratio arithmetic only — no weighting curves
- Voltage road assumes equal impedance at both readings
In short: Doubling a level is the whole decibel story: two power levels 1 W → 2 W sit 3.010300 dB apart (10·log10 of the ratio), while two voltages 1 V → 2 V sit 6.020600 dB apart (20·log10 — power scales with amplitude SQUARED, so the amplitude road pays the log twice). Run the road backwards and 10^(3.010300/10) returns exactly 2.000000×. And two identical sources never add to double the number: each +3.010300 dB, so 60 dB beside 60 dB is 63.010300 dB, not 120.
Formula
dB = 10·log10(P2 / P1) · dB = 20·log10(V2 / V1) · back: ratio = 10^(dB/10) power, 10^(dB/20) amplitude
A decibel is ten times the base-ten log of a POWER ratio — and twenty times the log of an AMPLITUDE ratio, because power rides the square of amplitude (P = V²/R) and the log of a square is twice the log. The factor of ten versus twenty is one idea, not two. Handy fixed points fall out of the definition: +10 dB is ten times the power BY DEFINITION, +20 dB is a hundred, +30 dB a thousand, and a doubling costs 3.010300 on the power road but 6.020600 on the amplitude road.
Worked Example
- Enter the two power levels you want compared.
- Read the power-road decibels, then run the road backwards from dB to the ratio.
- Enter two voltages and watch the amplitude road charge the log twice.
- Stack two identical sources and see why 60 + 60 lands at 63, not 120.
Defaults: 1 W → 2 W = 3.010300 dB power; 1 V → 2 V = 6.020600 dB amplitude; two of the 2 W source together read 6.020600 dB, not double.
Strengths & Limits Of This Model
Where this engine is strong
- Power and amplitude roads shown side by side
- The never-add rule priced, not asserted
Where it stops
- No A/C weighting or band filters
- No absolute references — pairs only
Practical Use Cases
Audio engineering
gain staging without the folklore
RF and signals
link budgets on one log ruler
Teaching
why 20·log and not 10·log
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Decibel Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
When do I use 10·log and when 20·log?
Use 10·log10 for quantities that ARE power or intensity (watts, W/m²), and 20·log10 for quantities whose SQUARE is power: voltage, current, sound pressure. The decibel was defined on power; the amplitude road is the same ruler reached through P ∝ V², and the log doubles the factor.
Why did my two decibel numbers not add?
Decibels are logarithms, and logarithms turn multiplication into addition — not addition into addition. Two identical sources double the POWER, and doubling costs 3.010300 dB on the power road: 60 dB + 60 dB = 63.010300 dB. To combine levels, convert each to a ratio, add the ratios, log the sum.
What is 3 dB, exactly?
Almost-but-not-quite a doubling: 10·log10(2) = 3.010300 dB. Engineering rounds it to 3 because the honest figure is awkward. This page keeps six decimals so the round trip closes: 10^(3.010300/10) reads back 2.000000.
Why is the amplitude doubling worth 6 dB and not 3?
Because doubling the voltage quadruples the power (P = V²/R with R held): 20·log10(2) = 6.020600 dB. The power DID quadruple; the amplitude merely doubled; both statements are the same fact on the same scale.
Where does the sound-pressure 20 µPa reference fit?
The sound intensity page logs intensity against 10⁻¹² W/m²; the sound-pressure road logs pressure against 20 µPa with the 20·log form — same scale, different measured quantity. That threshold-referenced question belongs to the sound intensity page; this page owns ratios between YOUR two levels.
Can a decibel be negative?
Happily — it just means the comparison lost. A filter with 1 W in and 0.5 W out reads −3.010300 dB. Negative decibels are losses, not errors; the log keeps its sign honest both directions.
What is the difference between dB and dBA?
dB is the raw ratio arithmetic this page performs; dBA is that arithmetic followed by a frequency weighting curve that mimics the ear at moderate levels. The weighting happens AFTER the logarithm and depends on the spectrum — it is a hearing question, not a ratio question, and this page does not pretend to do it.
Why does the same impedance matter for the voltage road?
The step from voltage ratio to power ratio divides by R twice — once for each V squared — and that cancels only when both readings see the same R. Compare a guitar pickup to a power amp directly and the 20·log shortcut lies; compare levels inside one system and it is exact.