Decibel Calculator
Calculate decibels from power or voltage ratios, convert between dB scales, and understand sound pressure levels.
Covers gain, loss, and SPL calculations.
What Is a Decibel? The decibel (dB) is a logarithmic unit used to express the ratio between two values. It was named after Alexander Graham Bell, inventor of the telephone (1876, United States). One bel equals a 10:1 power ratio; one decibel is one-tenth of a bel. The logarithmic scale is used because human perception of sound and signal strength is approximately logarithmic.
Power Ratio Formula dB = 10 x log10(P2 / P1). A 3 dB increase means the power has doubled. A 10 dB increase means the power has increased 10 times. A 20 dB increase means 100 times more power. A -3 dB means the power has halved.
Voltage/Amplitude Ratio Formula dB = 20 x log10(V2 / V1). Since power is proportional to voltage squared, the factor is 20 instead of 10. A 6 dB increase in voltage means roughly double the voltage. A 20 dB increase means 10 times the voltage.
Sound Pressure Level (SPL) Sound levels are measured in dB SPL, referenced to the threshold of human hearing (20 micropascals). Common levels: whisper = 30 dB, normal conversation = 60 dB, lawnmower = 90 dB, rock concert = 110 dB, threshold of pain = 130 dB. Every 10 dB increase sounds roughly twice as loud to the human ear.
Adding Decibels Because dB is logarithmic, you cannot simply add dB values. Two identical sound sources together produce 3 dB more (not double dB). To add: total = 10 x log10(10^(dB1/10) + 10^(dB2/10)). Two 80 dB sources together produce 83 dB, not 160 dB.
Applications Audio engineering uses dB for amplifier gain, speaker sensitivity, and mixing levels. Telecommunications uses dBm (referenced to 1 milliwatt) for signal strength. Electronics uses dB for filter response curves and antenna gain. Acoustics uses dB SPL for environmental noise measurement.