Decibel and Ratio Calculator
Convert power or root-power amplitude ratios to decibels and back. Add independent source levels that share a reference, using logarithmic power addition.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Use10log10 for a power ratio or20log10 for an amplitude whose square represents a power ratio. Independent source powers add in linear space, so convert levels to relative powers, add and convert back.
dB=10log10(P/P0)=20log10(A/A0); combined L=10log10Σ10^(Li/10)
Worked example
A power ratio2 is about3.0103dB. An amplitude ratio2 is about6.0206dB when the square-law relationship applies. Two independent60dB sources combine to about63.0103dB, not120dB.
Assumptions and input details
Decibels express a ratio. The20log rule requires a root-power quantity; voltage comparisons need the same relevant impedance. Power ratios are0 or1e−100–1e100; amplitude ratios0 or1e−50–1e50. Zero ratio is displayed as the−∞dB limit. Inverse gain inputs are finite−1000–1000dB. Level addition accepts2–20 finite inputs in that range and assumes the same reference and measurement conditions. Phase-coherent amplitudes cannot be added by this independent-power rule. A weighting or reference change is not performed; this is not a hearing-exposure assessment.
References: OpenStax sound intensity and level
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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