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Home›Electronics›Decibel dB Calculator

Decibel dB Calculator

Convert Between dB, Power Ratio, and Voltage Ratio

Select Mode

Ratio → dB dB → Ratio

Input (P2 or V2)

Reference (P1 or V1)

Power (10×log) Voltage (20×log)

Decibel Formulas

dB_power = 10 × log10(P2/P1)

dB_voltage = 20 × log10(V2/V1)

P2/P1 = 10^(dB/10) (power ratio)

V2/V1 = 10^(dB/20) (voltage ratio)

The decibel is a logarithmic unit used to express ratios. It is widely used in audio, RF, and signal processing because logarithmic scales match human perception and simplify multiplication (dB adds instead of ratios multiply). The 3dB point (half-power) defines filter bandwidth and amplifier frequency response.

⚠ Voltage and power use different dB formulas! Power: 10×log. Voltage: 20×log. 3dB power = 1.414× voltage (both represent 2× power). dBm = dB referenced to 1mW. 0dBm = 1mW, 30dBm = 1W.

Understanding Decibels

Decibels provide a convenient way to express large dynamic ranges. A power ratio of 1,000,000:1 is just 60dB. The human ear responds logarithmically to sound intensity. In electronics, dB is used for amplifier gain, filter attenuation, signal-to-noise ratio, and antenna gain. Adding 3dB doubles power; adding 10dB increases power 10×.

Power dB

dB = 10×log(P2/P1). +3dB = 2×. +10dB = 10×. +20dB = 100×. -3dB = 0.5× (half-power point).

Voltage dB

dB = 20×log(V2/V1). +6dB = 2× (4× power). +20dB = 10× (100× power). V2/V1 = 10^(dB/20).

Common References

dBm: 1mW reference. dBW: 1W reference. dBV: 1V RMS. dBμV: 1μV. dBi: isotropic antenna. dBd: dipole antenna.

Key Values

0dB = unity, 1dB = 1.26×, 3dB = 2×, 6dB = 4×, 10dB = 10×, 20dB = 100×, 40dB = 10,000×, 60dB = 1,000,000×.

Teaching Example: P2=200W, P1=100W (power ratio=2).
dB = 10 × log10(200/100) = 10 × log10(2) = 10 × 0.3010 = 3.01 dB.
Reverse: 3dB → power ratio = 10^(3/10) = 10^0.3 = 2.0.
Voltage example: V2=10V, V1=5V: dB = 20×log(2) = 6.02 dB. (4× power at same impedance).

Applications

Audio Engineering RF Design Filter Design Signal Analysis Telecom Systems

Frequently Asked Questions

What is dB?▼

Logarithmic ratio. Power: 10×log. Voltage: 20×log. 3dB = 2× power. 10dB = 10× power. Additive for cascaded stages.

dBm vs dB?▼

dB is a ratio. dBm is absolute power: 0dBm=1mW, 30dBm=1W. dBm + dB = dBm. dBm - dBm = dB (ratio).

What is -3dB?▼

-3dB = half power (0.5× power, 0.707× voltage). Defines bandwidth, cutoff frequency (fc), and half-power points in filters.

Why use log scale?▼

Human senses (hearing, sight) are logarithmic. dB compresses huge ranges (1 to 1M=60dB). Multiplication becomes addition. Cascaded gains add in dB.

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