A ratio of 1 (10·log₁₀(1) = 0). For absolute scales, 0 dBm = 1 mW, 0 dB SPL = 20 μPa = threshold of hearing, 0 dBV = 1 Vrms.

When do sound levels become dangerous?

OSHA hearing-damage limit: 8 hours at 85 dB SPL, halving exposure time for every +3 dB (90 dB = 4 hr, 95 dB = 2 hr, 100 dB = 1 hr). 130 dB SPL ≈ pain threshold. Concerts often run 110-115 dB.

Why is +3 dB "doubling"?

Power: 10·log₁₀(2) = 3.01... ≈ 3. So a 3 dB gain doubles power output. Voltage doubling is 6 dB (20·log₁₀(2) = 6.02). Common mnemonic source of confusion.

ISO 80000-3:2019 — Quantities and units, Acoustics. IEC 60027-3:2002 — Letter symbols for use in electrical technology — logarithmic and related quantities. ANSI S1.4 — Specification for sound level meters.

A ratio of 1 (10·log₁₀(1) = 0). For absolute scales, 0 dBm = 1 mW, 0 dB SPL = 20 μPa = threshold of hearing, 0 dBV = 1 Vrms.

When do sound levels become dangerous?

OSHA hearing-damage limit: 8 hours at 85 dB SPL, halving exposure time for every +3 dB (90 dB = 4 hr, 95 dB = 2 hr, 100 dB = 1 hr). 130 dB SPL ≈ pain threshold. Concerts often run 110-115 dB.

Why is +3 dB "doubling"?

Power: 10·log₁₀(2) = 3.01... ≈ 3. So a 3 dB gain doubles power output. Voltage doubling is 6 dB (20·log₁₀(2) = 6.02). Common mnemonic source of confusion.

ISO 80000-3:2019 — Quantities and units, Acoustics. IEC 60027-3:2002 — Letter symbols for use in electrical technology — logarithmic and related quantities. ANSI S1.4 — Specification for sound level meters.

Decibel Calculator (power · voltage · sound)

dB = 10·log₁₀(P₂/P₁) for power; 20·log₁₀(V₂/V₁) for voltage; absolute scales dBSPL / dBm / dBW / dBV / dBu.

Result

20.000 dB

Power ratio 100.0000 = 20.00 dB.

Modepower-ratio
Value 1 (ref)1.000000
Value 2100.000000
Decibel result20.0000 dB
InterpretationPower ratio 100.0000 = 20.00 dB.
+3 dBPower doubles (×2 power); voltage × √2 ≈ ×1.414
+6 dBVoltage doubles (×2 V); power × 4
+10 dBPower × 10
+20 dBVoltage × 10; power × 100
−3 dBPower halved (the "half-power" or "−3 dB point")

Step-by-step

dB = 10·log₁₀(100 / 1) = 10·log₁₀(100.0000) = 20.0000 dB.

How to use this calculator

Pick the dB type that matches your measurement: power-ratio (amplifier gain, antenna), voltage-ratio (audio signal), dB SPL (sound), dBm/dBV (absolute).
For ratio modes: enter reference + measured values.
For absolute modes: enter the single measured value in the natural unit (Pa for SPL, W for dBm, V for dBV).
The interpretation line places the result in a recognizable band (e.g. "rock concert" for 110 dB SPL).

About this calculator

The decibel (dB) is a LOGARITHMIC ratio. Power: 10·log₁₀(P₂/P₁). Voltage / amplitude: 20·log₁₀(V₂/V₁) — the factor of 20 (instead of 10) is because power ∝ V². For sound: dB SPL = 20·log₁₀(P/20 μPa), where 20 μPa is the reference threshold of human hearing. Absolute scales each have a fixed reference: dBm = ref 1 mW (RF + audio); dBV = ref 1 Vrms (consumer audio); dBu = ref 0.7746 Vrms (= √(0.6 mW into 600 Ω), pro audio "+4 dBu line level"); dBW = ref 1 W. Key benchmarks worth memorising: +3 dB doubles power; +6 dB doubles voltage; +10 dB = 10× power; +20 dB = 10× voltage = 100× power. The "−3 dB point" (half-power) is the standard cutoff in filter design.