About

Decibel miscalculations cascade through signal chains. A 3dB error doubles or halves actual power - amplifier stages compound this exponentially. This calculator implements the IEEE standard logarithmic definitions: 10log₁₀ for power ratios, 20log₁₀ for voltage ratios across matched impedances. The distinction matters because voltage squared equals power in resistive loads.

RF engineers sizing attenuator pads, audio technicians matching amplifier stages, and antenna designers calculating link budgets all require precise dB conversions. Manual calculation introduces transcription errors. The tool handles bidirectional conversion: input a ratio to find dB, or input dB to find the linear ratio. Results display both gain and attenuation interpretations since negative dB indicates signal loss.

Formulas

The decibel is a logarithmic unit expressing ratios. Power and voltage require different coefficients because power is proportional to voltage squared across constant impedance.

Power Gain: G_dB = 10 ⋅ log₁₀(P₂P₁)

Voltage Gain: G_dB = 20 ⋅ log₁₀(V₂V₁)

Inverse (Power Ratio from dB): P₂P₁ = 10^G_dB10

Inverse (Voltage Ratio from dB): V₂V₁ = 10^G_dB20

Where G_dB is the gain in decibels, P₁ and P₂ are input and output power, V₁ and V₂ are input and output voltage. The factor of 20 for voltage arises from P ∝ V², thus 10 ⋅ log₁₀(V²) = 20 ⋅ log₁₀(V).

Reference Data

dB Value	Power Ratio	Voltage Ratio	Common Application
0dB	1.000	1.000	Unity gain (no change)
1dB	1.259	1.122	Minimum audible difference
3dB	2.000	1.414	Half-power point (−3dB cutoff)
6dB	3.981	2.000	Voltage doubling
10dB	10.00	3.162	Order of magnitude power
12dB	15.85	3.981	Typical preamp gain stage
20dB	100.0	10.00	Voltage order of magnitude
30dB	1000	31.62	High-gain amplifier
40dB	10000	100.0	Antenna array gain
60dB	10⁶	1000	Dynamic range of quality audio
−3dB	0.501	0.708	Filter cutoff frequency
−6dB	0.251	0.501	Voltage halving
−10dB	0.100	0.316	Typical pad attenuator
−20dB	0.010	0.100	Significant attenuation
−40dB	0.0001	0.010	Noise floor suppression
−60dB	10⁻⁶	0.001	Background noise level
13.01dB	20.00	4.472	Power ratio of 20
26.02dB	400.0	20.00	Voltage ratio of 20
9.54dB	9.000	3.000	Triple voltage
4.77dB	3.000	1.732	Triple power

Frequently Asked Questions

Use 10×log₁₀ when comparing power values (watts, milliwatts). Use 20×log₁₀ when comparing voltage, current, or sound pressure values. The distinction exists because power is proportional to voltage squared (P = V²/R). When you square a ratio inside a logarithm, the coefficient doubles: 10×log(V²) = 20×log(V). Misapplying the coefficient produces errors of exactly 2× in the dB result.

Because 10×log₁₀(2) ≈ 3.01 dB. For voltage doubling across matched impedance, power quadruples (P ∝ V²), which equals 10×log₁₀(4) ≈ 6.02 dB. The 3 dB point specifically marks where power halves, used universally to define filter cutoff frequencies and amplifier bandwidth limits.

Add dB values directly. Three stages of +10 dB each yield +30 dB total. This logarithmic property makes dB convenient: multiplication of linear gains becomes addition of dB values. For a 10× amplifier followed by a 5× amplifier, the combined gain is 50×. In dB: 10 dB + 6.99 dB = 16.99 dB. Verify: 10^(16.99/10) ≈ 50.

Negative dB indicates attenuation (signal loss). A value of −6 dB means the output voltage is half the input voltage, or output power is one-quarter of input. Passive components like filters, cables, and attenuators produce negative dB values. An amplifier with −3 dB at 20 kHz indicates the high-frequency response drops to half-power at that frequency.

The 20×log formula for voltage assumes matched impedances. When source and load impedances differ, use the power formula or apply correction factors. For audio line levels (+4 dBu versus −10 dBV), the reference impedances differ: 600Ω for professional dBu, 10kΩ for consumer dBV. Direct voltage comparison without impedance context produces misleading dB values.

Standard practice uses one decimal place (e.g., 12.5 dB). Test equipment typically achieves ±0.1 dB accuracy. Two decimal places (12.53 dB) implies unrealistic precision for most applications. For cascaded calculations, maintain full precision internally and round only the final reported value to avoid accumulated rounding errors.