Decibel Calculator
Calculate decibels (dB) from power or voltage ratios. Switch between power mode (10×log) and voltage mode (20×log) to convert between linear ratios and logarithmic decibel values. See also our Signal to Noise Ratio Calculator and Sound Converter.
How to Calculate Decibels
The decibel (dB) is a logarithmic unit used to express the ratio between two values of a physical quantity, most commonly power or amplitude (voltage, current, sound pressure). Originally developed by Bell Telephone Laboratories in the 1920s, the decibel scale compresses large ratios into manageable numbers and aligns with human perception of sound intensity, which is also logarithmic.
To calculate decibels, you need a reference value and a measured value. For power quantities, use the formula dB = 10 × log₁₀(P₂/P₁). For field quantities like voltage, current, or sound pressure, use dB = 20 × log₁₀(V₂/V₁). The factor of 20 for voltage arises because power is proportional to voltage squared: 10 × log₁₀(V²) = 20 × log₁₀(V).
A positive dB value indicates gain (the measured value is larger than the reference), while a negative dB value indicates loss or attenuation. Key reference points: +3 dB means double the power, +10 dB means 10× the power, +20 dB means 100× the power. For voltage: +6 dB means double the voltage, +20 dB means 10× the voltage.
Decibel Formulas
Power Decibels:
dB = 10 × log₁₀(P₂/P₁)
P₂/P₁ = 10^(dB/10)
Voltage/Amplitude Decibels:
dB = 20 × log₁₀(V₂/V₁)
V₂/V₁ = 10^(dB/20)
Adding dB Values:
dB_total = dB₁ + dB₂ + dB₃ + ...
(equivalent to multiplying ratios)
Common Reference Levels:
dBm: reference = 1 mW
dBW: reference = 1 W
dBV: reference = 1 V
dBu: reference = 0.775 V
dB SPL: reference = 20 μPa
Example Calculation
An amplifier takes a 1W input signal and produces a 10W output. Calculate the gain in decibels:
Given: P₁ = 1W (input), P₂ = 10W (output)
dB = 10 × log₁₀(P₂/P₁) = 10 × log₁₀(10/1)
dB = 10 × log₁₀(10) = 10 × 1 = 10 dB
This is a 10 dB gain (10× power increase)
In voltage terms (assuming same impedance):
Voltage ratio = √(P₂/P₁) = √10 = 3.162
dB = 20 × log₁₀(3.162) = 20 × 0.5 = 10 dB ✓
Decibel Reference Table
| Decibels (dB) | Power Ratio | Voltage Ratio |
|---|---|---|
| -20 dB | 0.01 | 0.1 |
| -10 dB | 0.1 | 0.3162 |
| -6 dB | 0.2512 | 0.5012 |
| -3 dB | 0.5 | 0.7079 |
| 0 dB | 1 | 1 |
| 1 dB | 1.2589 | 1.1220 |
| 3 dB | 2 | 1.4142 |
| 6 dB | 3.9811 | 1.9953 |
| 10 dB | 10 | 3.1623 |
| 20 dB | 100 | 10 |
| 30 dB | 1000 | 31.623 |
| 40 dB | 10000 | 100 |
Frequently Asked Questions
What is a decibel?
A decibel (dB) is one-tenth of a bel, a logarithmic unit that expresses the ratio between two values. It is not an absolute unit like watts or volts — it always represents a ratio. The logarithmic scale is used because it compresses very large ranges (a trillion-fold in sound intensity) into manageable numbers (0-120 dB) and matches human perception, which is also logarithmic.
Why use 10×log for power and 20×log for voltage?
Power is proportional to voltage squared (P = V²/R). When you take the log of a squared quantity: 10×log₁₀(V²/V₁²) = 10×2×log₁₀(V₂/V₁) = 20×log₁₀(V₂/V₁). The factor of 20 ensures that the same physical change gives the same dB value whether you measure it as power or voltage. A 3 dB power increase equals a 3 dB voltage increase (√2 voltage ratio).
What does 3 dB mean?
3 dB represents a doubling (or halving) of power. In audio, +3 dB is barely perceptible to most listeners. In electronics, the -3 dB point defines the bandwidth of filters and amplifiers — it is the frequency where power drops to half (voltage drops to 1/√2 ≈ 0.707). This is also called the half-power point or cutoff frequency.
What is dBm and how does it differ from dB?
dBm is an absolute power level referenced to 1 milliwatt: dBm = 10×log₁₀(P/1mW). Unlike plain dB which is always a ratio, dBm tells you the actual power level. For example, 0 dBm = 1 mW, +10 dBm = 10 mW, +30 dBm = 1 W, -30 dBm = 1 μW. It is widely used in RF engineering, telecommunications, and fiber optics.
How do I add decibel values?
Adding dB values is equivalent to multiplying the linear ratios. If an amplifier has 20 dB gain and a cable has 3 dB loss, the net is 20 + (-3) = 17 dB. However, you cannot directly add dB values of independent signals (like two speakers). For that, convert to linear, add, then convert back: dB_sum = 10×log₁₀(10^(dB₁/10) + 10^(dB₂/10)). Two equal sources add to give +3 dB.
What are typical sound levels in decibels?
Threshold of hearing: 0 dB SPL, whisper: 30 dB, normal conversation: 60 dB, busy traffic: 80 dB, rock concert: 110 dB, threshold of pain: 130 dB, jet engine at 30m: 150 dB. Each 10 dB increase sounds roughly twice as loud to human ears. Prolonged exposure above 85 dB can cause hearing damage.
Decibel Scales in Different Fields
Different engineering fields use different reference levels with the decibel scale. In audio engineering, dBu (reference 0.775V) and dBV (reference 1V) are common for signal levels. In RF and telecommunications, dBm (reference 1mW) and dBW (reference 1W) express absolute power levels. In acoustics, dB SPL (reference 20 μPa) measures sound pressure level. In antenna engineering, dBi (reference isotropic radiator) and dBd (reference dipole) express antenna gain. Understanding which reference is being used is critical for correct interpretation.
Practical Applications
Decibels are used throughout electronics and physics: amplifier gain specifications, filter response curves, signal-to-noise ratios, link budgets in telecommunications, antenna patterns, acoustic measurements, vibration analysis, and seismology. The logarithmic scale makes it easy to calculate cascaded gains and losses by simple addition, and to visualize frequency responses on Bode plots where decades of frequency correspond to equal horizontal distances.