Decibel (dB) Calculator

About the Decibel (dB) Calculator

The Decibel (dB) Calculator converts between decibels and linear ratios for power, voltage/amplitude, and sound pressure levels. Decibels are a logarithmic unit used throughout electronics, acoustics, telecommunications, and signal processing to express ratios on a manageable scale.

For power ratios: dB = 10 × log₁₀(P₂/P₁). For voltage/amplitude ratios: dB = 20 × log₁₀(V₂/V₁). Sound pressure level (SPL): dB SPL = 20 × log₁₀(P/P₀), where P₀ = 20 µPa (threshold of hearing). Adding decibels of incoherent sources: L_total = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10)). Sound level decreases approximately 6 dB per doubling of distance from a point source.

Enter values to convert dB ↔ ratio, add multiple dB levels, or calculate distance attenuation for sound propagation. It gives you a fast reference when logarithmic units appear in audio, RF, or measurement work. That is especially handy when you need to confirm whether a gain or loss figure is being expressed in power or voltage terms.

When This Page Helps

Use this calculator when you need to move between decibels and linear ratios, combine noise sources, or estimate distance attenuation. It is useful in audio, RF, and instrumentation work where logarithmic units are standard. The side-by-side conversions make it easier to sanity-check a level change before you apply it. That helps avoid errors when the numbers look small but the ratio is large.

How to Use the Inputs

1. Select the mode: dB-to-ratio, ratio-to-dB, or SPL operations.
2. Enter a dB value or a linear ratio to convert.
3. Select power-type (10×log) or voltage-type (20×log) as applicable.
4. For SPL addition, enter two or more dB levels to combine.
5. For distance attenuation, enter source SPL and distances.
6. Review results and use the reference table for common values.

Example Calculation

Tips & Best Practices

• Memorize key values: 3 dB = 2× power, 10 dB = 10× power, 20 dB = 100× power.
• For voltage/amplitude: 6 dB ≈ 2×, 20 dB = 10×, 40 dB = 100×.
• Two identical sources add to +3 dB. Ten identical sources add to +10 dB.
• OSHA limits: 85 dBA for 8 hours. Every +5 dBA halves the allowed exposure time.
• Negative dB values are valid and common — they indicate attenuation (reduction).

The Decibel Scale

Alexander Graham Bell's original unit (bel = log₁₀ of power ratio) was too large for practical use, so the decibel (1/10 bel) became standard. The logarithmic scale compresses huge dynamic ranges into manageable numbers: human hearing spans a trillion-fold (10¹²) power range, which maps to 0-120 dB SPL.

The factor-of-10 difference between power dB (10×log) and voltage dB (20×log) comes from the power-voltage relationship P = V²/R. Since log(V²) = 2×log(V), the factor doubles.

Common Reference Levels

Different fields use different 0 dB reference points: dB SPL (20 µPa), dBm (1 mW into 50Ω or 600Ω), dBW (1 W), dBV (1 V RMS), dBu (0.775 V RMS, voltage that produces 1 mW into 600Ω), dBi (isotropic antenna gain), dBd (dipole antenna gain). Always specify the reference when giving absolute dB values.

Noise Addition and Incoherent Sources

When combining incoherent (independent) noise sources, powers add linearly: P_total = P₁ + P₂. This is why two 80 dB sources produce 83 dB, not 160 dB. For N identical sources at level L: L_total = L + 10×log₁₀(N). Coherent sources (phase-aligned) can add up to +6 dB (voltage addition) or cancel completely (destructive interference).

Frequently Asked Questions

• What does 3 dB mean?

  A 3 dB change is approximately a doubling (or halving) of power. Specifically, +3 dB = 2× power, -3 dB = 0.5× power. For voltage: +6 dB ≈ 2× voltage (because power ∝ V²). In acoustics, a 3 dB increase is barely perceptible to the human ear; 10 dB sounds roughly "twice as loud."

• How do I add two dB values?

  You cannot simply add dB values. You must convert to linear, add, then convert back. Two equal sources: adding 60 dB + 60 dB = 63 dB (not 120 dB). Formula: L_total = 10×log₁₀(10^(L₁/10) + 10^(L₂/10)). Shortcut: same level + same level = level + 3 dB.

• What are dBm and dBW?

  dBm = dB relative to 1 milliwatt. 0 dBm = 1 mW. dBW = dB relative to 1 watt. 0 dBW = 1 W = 30 dBm. Common Wi-Fi power: +20 dBm = 100 mW. Cell phone: +23 dBm = 200 mW. These are absolute power levels, not ratios.

• What are dBA and dBC?

  dBA uses A-weighting, which filters sound to match human ear sensitivity (reduced sensitivity to low and very high frequencies). dBC uses C-weighting, which is nearly flat (good for measuring peak/impulse sounds). Occupational noise limits (e.g., OSHA 85-90 dBA) use A-weighting.

• How loud is 120 dB?

  0 dB SPL = threshold of hearing. 30 dB = whisper. 60 dB = conversation. 85 dB = heavy traffic (hearing damage begins with prolonged exposure). 100 dB = power tools. 120 dB = jet engine at 100m (pain threshold). 140 dB = firecracker/gunshot (immediate damage). 194 dB = theoretical maximum in air.

• Does sound really drop 6 dB per doubling of distance?

  For a point source in free field (no reflections), yes: SPL drops 6 dB per doubling of distance (inverse square law). Line sources (highways, trains) drop only 3 dB per doubling. Indoor environments have reflections that reduce the drop rate. The 6 dB rule is the theoretical ideal.