Decibel Calculator

Convert between decibels (dB), power ratios, voltage ratios, and absolute power levels (dBm). Supports both power and voltage/current calculations.

Decibel Formulas: Power Ratio to dB: dB = 10 × log₁₀(P₂/P₁) Voltage/Current Ratio to dB: dB = 20 × log₁₀(V₂/V₁) dB = 20 × log₁₀(I₂/I₁) (assumes equal impedances) dB to Power Ratio: P₂/P₁ = 10^(dB/10) dB to Voltage Ratio: V₂/V₁ = 10^(dB/20) Absolute Power (dBm): dBm = 10 × log₁₀(P_mW / 1 mW) P_mW = 10^(dBm/10) Other Absolute References: dBW = 10 × log₁₀(P_W / 1 W) dBV = 20 × log₁₀(V / 1 V) dBu = 20 × log₁₀(V / 0.775 V) Conversions: dBW = dBm - 30 dBm = dBW + 30 dBu = dBV + 2.2 Common Values: +3 dB = 2× power = 1.41× voltage +6 dB = 4× power = 2× voltage +10 dB = 10× power = 3.16× voltage +20 dB = 100× power = 10× voltage -3 dB = 0.5× power = 0.707× voltage -10 dB = 0.1× power = 0.316× voltage Cascading Systems: Total dB = dB₁ + dB₂ + dB₃ + ... (add dB values, don't multiply)
Example 1 (Amplifier Gain - Power): Input: 1 mW, Output: 100 mW dB = 10 × log₁₀(100/1) = 10 × log₁₀(100) dB = 10 × 2 = 20 dB gain Example 2 (Amplifier Gain - Voltage): Input: 0.1 V, Output: 3.16 V dB = 20 × log₁₀(3.16/0.1) = 20 × log₁₀(31.6) dB = 20 × 1.5 = 30 dB gain Example 3 (Cable Loss): Input: 100 mW, Output: 50 mW dB = 10 × log₁₀(50/100) = 10 × log₁₀(0.5) dB = 10 × (-0.301) = -3 dB loss Example 4 (dBm to Power): WiFi transmitter: 20 dBm P = 10^(20/10) = 10² = 100 mW In watts: 0.1 W Example 5 (Power to dBm): Cell phone: 1 W = 1000 mW dBm = 10 × log₁₀(1000) = 10 × 3 = 30 dBm Example 6 (Cascaded Amplifiers): Amp 1: +25 dB, Amp 2: +15 dB Total gain = 25 + 15 = 40 dB Voltage ratio = 10^(40/20) = 100× Power ratio = 10^(40/10) = 10,000× Example 7 (Antenna System): Transmitter: 30 dBm (1 W) Cable loss: -3 dB Antenna gain: +9 dBi Effective radiated power: 30 - 3 + 9 = 36 dBm = 3.98 W ERP Example 8 (Audio Level Conversion): Pro audio: +4 dBu = 0.775 × 10^(4/20) V = 0.775 × 1.585 = 1.228 V RMS Consumer line level: -10 dBV V = 1 × 10^(-10/20) = 0.316 V RMS Example 9 (Filter Cutoff - 3 dB Point): Input voltage: 2 V Output at cutoff: 2/√2 = 1.414 V dB = 20 × log₁₀(1.414/2) dB = 20 × log₁₀(0.707) = -3 dB Example 10 (Signal-to-Noise Ratio): Signal: 10 mW, Noise: 0.01 mW SNR = 10 × log₁₀(10/0.01) SNR = 10 × log₁₀(1000) = 30 dB Example 11 (From dB to Ratio): Attenuator: -20 dB Power ratio = 10^(-20/10) = 0.01 Output is 1% of input (99% loss) Example 12 (Microphone Sensitivity): Mic output: -60 dBV at 1 Pa SPL V = 10^(-60/20) = 0.001 V = 1 mV

What is a decibel (dB)?

A decibel is a logarithmic unit expressing the ratio between two values. It's used to measure power, voltage, sound intensity, and signal strength. Because it's logarithmic, dB compresses large ranges: 3 dB = 2× power, 10 dB = 10× power, 20 dB = 100× power.

What is the difference between dB power and dB voltage?

Power dB uses factor of 10: dB = 10 log₁₀(P₂/P₁). Voltage/current dB uses factor of 20: dB = 20 log₁₀(V₂/V₁) because power is proportional to voltage squared (P ∝ V²). For equal impedances, 6 dB voltage gain = 2× voltage = 4× power.

Why are dB values sometimes negative?

Negative dB indicates a decrease or loss. 0 dB = no change (ratio of 1:1). Positive dB = gain/increase. Negative dB = attenuation/loss. For example, -3 dB means power reduced to 50%, -10 dB means power reduced to 10%.

What is dBm and how is it different from dB?

dBm is absolute power referenced to 1 milliwatt: dBm = 10 log₁₀(P/1mW). 0 dBm = 1 mW, 30 dBm = 1 W. dB is relative (ratio), while dBm is absolute power. dBm is common in RF/telecommunications. Adding dB to dBm gives dBm: 10 dBm + 3 dB = 13 dBm.

What does 3 dB mean in practical terms?

3 dB is significant: +3 dB = double power, -3 dB = half power. In voltage (same impedance), +6 dB = double voltage. 3 dB is also the filter cutoff point (half-power frequency). Audio: -3 dB is barely noticeable volume reduction.

How do I add decibels?

When cascading systems, ADD decibels (don't multiply). If amplifier 1 has +20 dB gain and amplifier 2 has +15 dB gain, total gain is 20 + 15 = 35 dB. This is because dB is logarithmic: log(A×B) = log(A) + log(B). Ratios multiply, dB values add.

What is dBV, dBu, and dBFS?

dBV: voltage referenced to 1V RMS (0 dBV = 1V). dBu: voltage referenced to 0.775V RMS (0 dBu = 0.775V, professional audio). dBFS: digital full scale, 0 dBFS = maximum digital value, all values are negative or zero to avoid clipping.

What are common dB reference levels?

Audio: 0 dBu = 0.775V, line level ≈ -10 dBV (consumer) or +4 dBu (pro). RF: 0 dBm = 1 mW. Sound: 0 dB SPL = 20 µPa (threshold of hearing). Antennas: dBi (isotropic reference), dBd (dipole reference). WiFi: typically 15-20 dBm.

How do dB relate to human perception?

Humans perceive logarithmically. Sound: +10 dB SPL ≈ 2× perceived loudness. Light: similar logarithmic perception. Phone signal: -70 dBm is good, -100 dBm is weak but usable, -110 dBm is near unusable. Each -10 dB makes signal harder to detect.

What is a typical amplifier gain in dB?

Audio preamps: 20-60 dB (10× to 1000× voltage). Power amps: 20-40 dB. Op-amps: 60-120 dB open-loop gain. RF LNAs: 10-20 dB. Antenna gain: 2-15 dBi (omnidirectional to directional). Total system gain is sum of all stages in dB.

How do I convert between different dB references?

dBm to dBW: dBW = dBm - 30. dBV to dBu: dBu = dBV + 2.2. dBi to dBd: dBd = dBi - 2.15. These conversions involve adding/subtracting constants because all are logarithmic scales with different reference points.

What is signal-to-noise ratio (SNR) in dB?

SNR (dB) = 10 log₁₀(Signal Power/Noise Power). Higher is better. 0 dB SNR = signal equals noise. 10 dB SNR = signal 10× stronger than noise (acceptable for some uses). 20 dB = good. 40+ dB = excellent. Audio CDs have ~96 dB SNR (16-bit).

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