🔊 Decibel Calculator

The decibel (dB) is a logarithmic unit used to express the ratio between two values, most commonly power or voltage levels. It was named after Alexander Graham Bell and uses a base-10 logarithm: a ratio of 10:1 in power equals 10 dB, 100:1 equals 20 dB, and 1000:1 equals 30 dB. The logarithmic scale is used because human perception of loudness (and many other sensations) is approximately logarithmic—a 10 dB increase sounds about "twice as loud" to human ears.

The key formulas are: Power ratio in dB = 10 × log₁₀(P₂ / P₁) and Voltage ratio in dB = 20 × log₁₀(V₂ / V₁). The factor of 20 (not 10) for voltage comes from power being proportional to voltage squared (P = V²/R), and squaring doubles the logarithm.

The decibel is always a ratio, not an absolute value. To express absolute levels, dB is referenced to a known value:

Common reference points: 0 dBm = 1 mW; 10 dBm = 10 mW; 20 dBm = 100 mW; 30 dBm = 1 W; 60 dBm = 1 kW. Room conversation is about 60 dB SPL, a rock concert is 110-120 dB SPL, and the threshold of pain is around 130 dB SPL.

1. Choose the conversion direction: ratio to dB, or dB to ratio.
2. Select whether you are working with power or voltage ratios.
3. Enter the value (ratio or dB) to convert.
4. Click Calculate to see the converted value.
5. Use the dBm/dBW reference table for absolute power calculations.

Why is the dB formula different for power (10log) and voltage (20log)?

Power is proportional to voltage squared (P = V²/R). When you take the log of V², you get 2×log(V). So 10×log(P₂/P₁) = 10×log(V²/V±²) = 20×log(V₂/V₁), assuming the same impedance. The factor of 20 (vs 10) for voltage is simply the squaring relationship between voltage and power.

What is 0 dBm in watts?

0 dBm = 1 mW = 0.001 W. The formula is P(W) = 10^(dBm/10) / 1000. So 10 dBm = 10 mW, 20 dBm = 100 mW, 30 dBm = 1 W, and -10 dBm = 0.1 mW. This is the standard reference in RF engineering for expressing absolute power levels.

What does a 3 dB change mean?

A 3 dB increase represents approximately double the power (10^0.3 = 1.995 ≈ 2). A 3 dB decrease halves the power. For voltage, 3 dB is a factor of √2 ≈ 1.414. This is a rule of thumb: 3 dB = 2× power, 6 dB = 4× power, 10 dB = 10× power, 20 dB = 100× power.

How loud is 85 dB SPL and is it safe?

85 dB SPL is roughly the noise level of heavy traffic or a noisy restaurant. Prolonged exposure (8+ hours) at 85 dB can cause gradual hearing damage. OSHA limits workplace noise to 90 dB for 8 hours, but NIOSH recommends 85 dB. At 100 dB, damage can occur in 15 minutes; at 120 dB, instantly.

How do I add dB values from cascaded stages?

Simply add them algebraically. An amplifier with 20 dB gain, a cable with 2 dB loss, and a filter with 1 dB loss give a net gain of 20 - 2 - 1 = 17 dB. This additive property is one of the main advantages of the dB scale—it replaces multiplication of ratios with addition of dB values.

What is the difference between dB and dBm?

dB is a ratio (relative), while dBm is an absolute power level referenced to 1 milliwatt. "This amplifier has 20 dB gain" means it multiplies power by 100×. "This transmitter outputs 20 dBm" means it outputs 100 mW. You can add dB values to dBm: a 20 dBm signal amplified by 10 dB becomes 30 dBm (1 W).

The 3 dB rule: a 3 dB change is approximately a 2:1 power ratio (1.995:1 precisely) or 1.414:1 voltage ratio. Each additional 3 dB roughly doubles the power again. The 10 dB rule: a 10 dB increase sounds approximately "twice as loud" to human ears, but represents exactly 10× the power. When cascading gain/loss stages (amplifier + filter + cable), simply add the dB values: a 20 dB amplifier followed by a -3 dB cable loss yields net 17 dB gain. Negative dB values represent attenuation or loss. In RF link budgets, sum all gains and losses to find the received signal level. The noise floor of a spectrum analyzer might be -150 dBm/Hz; a strong WiFi signal is about -40 dBm; a GPS satellite signal arriving at Earth is about -130 dBm—one hundred trillion times weaker than 1 mW. For SNR (signal-to-noise ratio), subtract noise dB from signal dB: a -40 dBm signal with -100 dBm noise gives 60 dB SNR.