About

Miscalculating decibel values in signal chain design leads to clipped amplifiers, damaged speakers, or failed RF link budgets. The decibel is a dimensionless logarithmic ratio, not a linear unit. A 3 dB gain doubles power but only increases voltage by factor 1.414. Confusing power-referenced and voltage-referenced formulas is the single most common source of error. This calculator implements both 10 log (power) and 20 log (voltage/amplitude) conversions, incoherent dB addition for combining independent sources, and absolute-level conversions between dBm, dBW, dBV, dBu, and linear watts or volts. All results assume resistive (matched-impedance) conditions. For reactive loads the voltage-to-power relationship requires impedance correction that this tool does not apply.

Formulas

The decibel expresses the ratio of two quantities on a logarithmic scale. The factor depends on whether the quantity is power-like or root-power (field/amplitude) in nature.

dB = 10 ⋅ log₁₀(P₁P₀)

For voltage, current, or sound pressure (root-power quantities measured across identical impedance):

dB = 20 ⋅ log₁₀(V₁V₀)

To combine n incoherent (uncorrelated) sources expressed in decibels:

dB_total = 10 ⋅ log₁₀(n∑i=1 10^{dB_i / 10})

Absolute power unit dBm (referenced to 1 mW):

P (W) = 10^{(dBm − 30) / 10}

dBm = 10 ⋅ log₁₀(P) + 30

Where P₁ = measured power, P₀ = reference power, V₁ = measured voltage, V₀ = reference voltage, P = power in W, dB_i = individual source level in dB.

Reference Data

Unit	Reference	Quantity	Formula	Typical Use
dB	Ratio (dimensionless)	Power or Voltage	10 log₁₀(P₁/P₀) or 20 log₁₀(V₁/V₀)	Gain/loss in any system
dBm	1 mW	Power	10 log₁₀(P / 0.001)	RF, telecom, Wi-Fi
dBW	1 W	Power	10 log₁₀(P / 1)	Broadcast transmitters
dBV	1 V_RMS	Voltage	20 log₁₀(V / 1)	Audio line levels
dBu	0.7746 V_RMS	Voltage	20 log₁₀(V / 0.7746)	Professional audio
dB SPL	20 μPa	Sound pressure	20 log₁₀(p / 20×10⁻⁶)	Acoustics
dBFS	Full-scale digital	Amplitude	20 log₁₀(A / A_max)	Digital audio
dBi	Isotropic radiator	Power (antenna gain)	10 log₁₀(G)	Antenna specifications
dBd	Half-wave dipole	Power (antenna gain)	dBi − 2.15	Amateur radio
dBμV	1 μV	Voltage	20 log₁₀(V / 10⁻⁶)	EMC, antenna measurements
dBc	Carrier signal level	Power	10 log₁₀(P_spur / P_carrier)	Spurious emissions
Common dB ↔ Ratio Quick Reference
0 dB	Power ratio: 1		Voltage ratio: 1
1 dB	Power ratio: 1.259		Voltage ratio: 1.122
3 dB	Power ratio: 1.995 (≈ 2×)		Voltage ratio: 1.413
6 dB	Power ratio: 3.981		Voltage ratio: 1.995 (≈ 2×)
10 dB	Power ratio: 10		Voltage ratio: 3.162
20 dB	Power ratio: 100		Voltage ratio: 10
30 dB	Power ratio: 1000		Voltage ratio: 31.62
40 dB	Power ratio: 10,000		Voltage ratio: 100
−3 dB	Power ratio: 0.501 (half)		Voltage ratio: 0.708
−6 dB	Power ratio: 0.251		Voltage ratio: 0.501 (half)
−10 dB	Power ratio: 0.1		Voltage ratio: 0.316
−20 dB	Power ratio: 0.01		Voltage ratio: 0.1

Frequently Asked Questions

Use 10 × log₁₀ for power quantities (watts, intensity, power spectral density). Use 20 × log₁₀ for root-power (field) quantities such as voltage, current, or sound pressure. The factor of 20 arises because power is proportional to the square of the field quantity (P ∝ V²), so 10 log(V²) = 20 log(V). This equivalence holds only when both measurements share the same impedance.

No. Because decibels are logarithmic, you cannot add them linearly. Two identical sources at 90 dB each do not produce 180 dB. For incoherent (uncorrelated) sources, convert each to linear power, sum, then convert back: the result is approximately 93 dB. The calculator's dB Addition mode performs this correctly using 10 log₁₀(10^dB₁/10 + 10^dB₂/10).

dBm references 1 mW and is standard in RF and telecom. dBW references 1 W, so 0 dBW = 30 dBm. dBV references 1 V_RMS and is used in consumer audio. dBu references 0.7746 V_RMS (the voltage that delivers 1 mW into 600 Ω) and is the professional audio standard. Converting between them requires knowing the reference and quantity type.

A negative decibel value indicates attenuation (loss). If the measured quantity is smaller than the reference, the ratio is less than 1 and log₁₀ of a number less than 1 is negative. For example, halving power yields −3 dB. This is normal and expected in filter design, cable loss calculations, and any attenuating system.

The 20 log voltage-to-dB conversion assumes equal impedance at both measurement points. If impedances differ, the voltage ratio no longer directly maps to the power ratio. In such cases you must calculate power explicitly: P = V² ÷ Z, then use the 10 log power formula. This tool assumes matched impedance for voltage conversions.

All computations use IEEE 754 double-precision floating point via JavaScript's native Math.log10 and Math.pow, providing approximately 15 significant digits of precision. Results are displayed rounded to 6 decimal places. For metrology-grade work requiring uncertainty budgets, dedicated calibration software is recommended.