Decibel Calculator: dB Power, dBSPL, dBm, Source Summation

Compute dB (10·log P/P₀ or 20·log V/V₀), sound pressure level SPL, dBm/dBW/dBu and source summation in dB. Logarithmic scale with standard references.

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The decibel

The decibel (dB) is a logarithmic unit expressing the ratio between two quantities — typically a measured value and a reference. Introduced in the 1920s at Bell Labs to quantify attenuation on telephone lines (hence the name, after Alexander Graham Bell), it's now universal in acoustics, electronics, telecoms, seismology, photography. For a power quantity (P, W, energy): L = 10 · log₁₀(P/P_ref). For an amplitude quantity (voltage V, sound pressure p, current): L = 20 · log₁₀(A/A_ref). The factor 20 comes from power ∝ amplitude² (P ∝ V²), so log(V²) = 2·log(V).

Why logarithmic

The dB scale compresses enormous ranges into manageable numbers. The human ear perceives sound intensities over a 10¹² range (hearing threshold 10⁻¹² W/m² vs pain threshold 1 W/m²), which maps to 0-120 dBSPL. Adding dB corresponds to multiplying linear ratios: +3 dB ≈ doubling power; +6 dB ≈ doubling amplitude; +10 dB = ×10 power; +20 dB = ×10 amplitude; −3 dB = half power.

Sound pressure level (SPL)

The sound pressure level (SPL) is expressed in dBSPL with reference p₀ = 20 μPa (hearing threshold at 1 kHz): L = 20·log₁₀(p/p₀). Typical values: 0 dBSPL hearing threshold (~20 μPa); 30 dB quiet room; 60 dB conversation; 80 dB city traffic; 90 dB vacuum cleaner; 100 dB rock concert at distance; 110 dB jackhammer; 120 dB pain threshold / jet takeoff; 140 dB eardrum rupture. Prolonged exposure above 85 dB can cause permanent hearing damage.

Weighted decibels

The human ear isn't uniformly sensitive to all frequencies: more sensitive at 2-5 kHz, less at 20 Hz and 20 kHz. For environmental assessments weighting filters are used: dBA (A-scale, most common, weights according to mean sensitivity at ~60 dB); dBC (nearly flat, for low-frequency high-level noise); dBZ (unweighted). Occupational exposure limits LEX,8h are typically set at 80-87 dBA. Phones report dBA; concerts dBC (to capture the bass).

Related units

  • dBm: power referenced to 1 mW. 0 dBm = 1 mW; 30 dBm = 1 W; −30 dBm = 1 μW. Widely used in RF and optical telecoms.
  • dBW: power referenced to 1 W. 0 dBW = 1 W = 30 dBm.
  • dBu: voltage referenced to 0.7746 V RMS (= 1 mW into 600 Ω). Pro-audio standard.
  • dBV: voltage referenced to 1 V RMS. Consumer audio.
  • dBFS: digital full-scale. 0 dBFS = max representable; always negative or zero.
  • dBi: antenna gain referenced to ideal isotropic antenna.
  • dBc: ratio relative to carrier (in RF).

Source summation

Two identical in-phase sources produce +3 dB (power doubles). General formula for incoherent summation (uncorrelated sources): L_tot = 10 · log₁₀(Σ 10^(L_i/10)). Example: 60 + 60 dB = 10·log(2·10⁶) ≈ 63 dB (not 120!). 60 + 70 dB: ≈ 70.4 dB (loudest source dominates). Differences ≥ 10 dB render the weaker source negligible.

Technical applications

Audio: mixer levels (0 VU = −18 dBFS; 0 dBFS = clip); instrument dynamic range; amplifier gain; EQ attenuation. Telecoms: radio link budget (Tx + antenna − path loss + Rx antenna = received power); fibre attenuation (~0.2 dB/km at 1550 nm); receiver sensitivity. Acoustics: wall insulation R_w dB; reverberation time RT60; absorption coefficients. Seismology: Richter magnitude is a similar log scale.

How to use

Four modes: from power (P, P_ref → dB); from amplitude (V/pressure, V_ref → dB); dB to ratio (dB → P/P_ref or A/A_ref); source summation (comma-separated L_i dB list → L_tot). For SPL enter pressure in Pa with p₀ = 20 μPa reference (default). For dBm enter power in mW. Scientific notation supported (1e-3 = 0.001).

Updated July 2026

Frequently Asked Questions

What is a decibel?

It is a logarithmic unit expressing the ratio between two quantities, not an absolute value. For power L = 10·log₁₀(P/P₀), for amplitudes (voltage, pressure) L = 20·log₁₀(A/A₀). The logarithmic scale compresses huge ranges: human hearing spans a power ratio of a trillion, about 120 dB.

Why is 10 used for power and 20 for amplitude?

Because power is proportional to the square of amplitude (P ∝ A²), and log(A²) = 2·log(A). So 20·log(A/A₀) = 10·log(A²/A₀²) = 10·log(P/P₀): the two formulas give the same number of dB for the same physical change. The calculator uses the correct factor based on the quantity you enter.

What does a 3 dB and a 10 dB increase mean?

3 dB corresponds to a doubling of power (10^0.3 ≈ 2), 10 dB to ten times the power. For amplitude, instead, 6 dB doubles the value. In acoustics a 10 dB increase is perceived as a doubling of subjective loudness, even though the sound power is ten times higher.

How do you add several sound sources in decibels?

Not arithmetically: convert to powers, add, and return to dB with L = 10·log₁₀(Σ 10^(Lᵢ/10)). Two 80 dB sources give not 160 dB but 83 dB: doubling the sources always adds 3 dB. The calculator performs this energy summation for any number of sources.

What are dBSPL, dBm and dBFS?

They are decibels referenced to standard values: dBSPL measures sound pressure relative to 20 µPa (the hearing threshold), dBm power relative to 1 milliwatt (used in radio and telecom), dBFS the digital level relative to full scale. The decibel alone is a ratio: an absolute value always needs a reference.

How many decibels are dangerous to hearing?

Prolonged exposure above 85 dBSPL can damage hearing: it is the legal limit for workplaces. A rock concert reaches 110 dB, the pain threshold is around 130 dB. Every extra 3 dB halves the safe exposure time, following the equal-energy principle adopted by regulations.

Is the decibel used only for sound?

No: it originated in telecommunications (from the bel, named after Alexander Graham Bell) to measure the attenuation of telephone lines. Today it is used for amplifier gain, signal-to-noise ratio, cable attenuation, antenna gain (dBi) and in optics for fibres. Anywhere ratios span many orders of magnitude.

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