Convert dB to ratio

Q: Is 3dB or 6dB "double"?

Both are, but of different quantities. 3dB doubles power; 6dB doubles voltage. A filter cutoff at −3dB is where power halves, which corresponds to 0.707 in voltage.

Convert decibels (dB) into a linear ratio. Example: −3 dB = 0.707× (voltage)

Decibels

Voltage ratio

1×

Power ratio

1×

History

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Formula

Voltage ratio: ratio = 10^(dB/20)
Power ratio: ratio = 10^(dB/10)
Example: −3 dB → voltage ratio ≈ 0.707 (= 1/√2), power ratio = 0.5

Design notes

The decibel is a logarithmic unit used for amplifier gain, filter attenuation, antenna gain and much else. Human hearing is logarithmic too, which is why audio work uses the same scale.

Values worth knowing by heart:
• 0 dB → 1× (no change)
• −3 dB → 0.707× in voltage, 0.5× in power — this is the definition of a cutoff frequency
• −6 dB → 0.5× (voltage)
• −20 dB → 0.1× (voltage)
• +6 dB → 2× (voltage)

When you need this

For amplifier gain, filter attenuation, antenna gain and signal-to-noise ratio — working out what a figure quoted in dB actually multiplies by. Voltage and power ratios are shown together so you cannot misread which basis applies.

Voltage and power use different factors

dB is a logarithmic ratio, but power uses 10·log₁₀ and voltage uses 20·log₁₀. Into the same resistance, power goes as the square of voltage, hence the factor of two.

So the same "6dB" means twice the voltage but four times the power. Always establish what quantity a specification is referring to.

Worth memorising

dB	Voltage ratio	Power ratio	Feel
1 dB	1.12	1.26	Just about perceptible
3 dB	1.41 (√2)	2.00	Power doubles / halves
6 dB	2.00	3.98	Voltage doubles
10 dB	3.16	10.0	Power up one decade
20 dB	10.0	100	Voltage up one decade
40 dB	100	10,000	Voltage up two decades
60 dB	1,000	1,000,000	Voltage up three decades
−3 dB	0.707	0.500	Filter cutoff
−20 dB	0.1	0.01	Attenuated tenfold

With "20dB is ten times in voltage" and "6dB is twice in voltage" you can build the rest by addition: 26dB is 10×2 = 20 times, 46dB is 10×10×2 = 200 times.

dB with a reference

Absolute units rather than plain ratios.
Unit	Reference	Where used
dBm	1 mW	RF power. 0dBm = 1mW, 30dBm = 1W
dBW	1 W	High power. 0dBW = 1W = 30dBm
dBµV	1 µV	EMC measurement voltage
dBµV/m	1 µV/m	Radiated emission field strength
dBi	Isotropic radiator	Antenna gain
dBc	The carrier	Spurious emissions, phase noise

Frequently asked questions

Is 3dB or 6dB "double"?

Both are, but of different quantities. 3dB doubles power; 6dB doubles voltage. A filter cutoff at −3dB is where power halves, which corresponds to 0.707 in voltage.

How do I convert dBm to watts?

dBm references 1mW, so use the power ratio: P[mW] = 10^(dBm/10). 0dBm = 1mW, 20dBm = 100mW, 30dBm = 1W. That is how you read a BLE transmit power of 0dBm or a WiFi figure of 20dBm.

Why is EMC measured in dBµV/m?

The range of field strengths involved spans more than six decades, from µV/m to V/m. A logarithmic scale lets limits and measurements share one plot. 40dBµV/m is 100µV/m.

What does a negative dB mean?

A ratio below one, i.e. attenuation. −20dB is a tenth in voltage and a hundredth in power. It is how filter stopbands and cable losses are expressed.

Standards and references

IEC 60027-3 — Definition of logarithmic quantities and their units (dB / Np).
CISPR 16-1-1 — EMC measuring equipment specification; use of dBµV.

Last updated: 2026-08-29