What is a decibel (dB)?

A decibel is a logarithmic unit that expresses the ratio between two values of a physical quantity. It is not an absolute unit — it always describes a ratio relative to a reference. For voltage: dB = 20 × log₁₀(Vout/Vin). For power: dB = 10 × log₁₀(Pout/Pin). Decibels are used in audio, RF, filters, and signal processing.

What is the difference between dB for power and voltage?

Because power is proportional to voltage squared (P = V²/R), doubling voltage quadruples power. To keep the dB scale consistent, voltage uses 20·log₁₀ and power uses 10·log₁₀. A 6dB change means ×2 voltage but ×4 power. A 3dB change means ×√2 ≈ 1.41× voltage but exactly ×2 power.

+3dB means the power doubles (×2) and voltage increases by ×1.414 (√2). −3dB means the power is halved (×0.5) and voltage is 70.7% of the original. The −3dB point is the standard definition of a filter cutoff frequency — at this frequency, half the input power reaches the output.

0 dBm is defined as 1 milliwatt of power. The "m" suffix means the reference is 1mW. So 10dBm = 10mW, 20dBm = 100mW, 30dBm = 1W. Negative values: −10dBm = 0.1mW, −30dBm = 1µW. dBm is the standard unit for RF signal levels. 0dBm into 50Ω corresponds to about 224mV RMS.

How do I convert dB to a voltage ratio?

Use the formula: voltage ratio = 10^(dB / 20). For −20dB: 10^(−20/20) = 10^(−1) = 0.1. This means the output voltage is 1/10th of the input. For +6dB: 10^(6/20) = 10^0.3 ≈ 2.0, so the output is twice the input voltage.

What is the difference between dBm, dBV and dBu?

dBm: power relative to 1mW (standard in RF). dBV: voltage relative to 1V RMS (used in audio/electronics). dBu: voltage relative to 0.775V RMS, which is the voltage that produces 1mW in a 600Ω load — a legacy standard from telephone systems still used in professional audio. 0dBu ≈ −2.2dBV.

Why is −3dB the standard filter cutoff point?

−3dB is the frequency where the output power is exactly half the input power. It is also the point where the imaginary and real parts of the filter transfer function are equal — a natural mathematical boundary. This happens at f₀ = 1/(2πRC) for an RC filter. Engineers chose it as the standard cutoff because half-power is a clear, unambiguous definition.

How many dB is doubling the power?

Doubling the power is +3dB, since 10 × log₁₀(2) ≈ 3.01dB. Doubling the voltage is +6dB, since 20 × log₁₀(2) ≈ 6.02dB. These are worth memorizing: every +3dB doubles the power, every +10dB multiplies it by 10, and every +20dB multiplies voltage by 10.

dB Converter

Convert between decibels and voltage / power ratios in both directions.

Enter dB value

Decibels (dB)

Common values

Results

dB (voltage ref)3.000 dB

dB (power ref)3.000 dB

Voltage ratio1.413 ×

Power ratio1.995 ×

% of input (V)141.3 %

Formulas

dB (voltage ref)

dB = 20 · log₁₀(Vout / Vin)

dB (power ref)

dB = 10 · log₁₀(Pout / Pin)

Ratio from dB

ratio = 10^(dB/20) [voltage]

Common dB Reference Values

dB	Voltage Ratio	Power Ratio	Meaning
-20 dB	0.1×	0.01×	1/10 voltage, 1/100 power
-10 dB	0.316×	0.1×	1/10 power
-6 dB	0.5×	0.25×	Half voltage
-3 dB	0.707×	0.5×	Half power (-3 dB point)
0 dB	1×	1×	No change (unity)
+3 dB	1.414×	2×	Double power
+6 dB	2×	4×	Double voltage
+10 dB	3.162×	10×	10× power
+20 dB	10×	100×	10× voltage, 100× power
+40 dB	100×	10000×	100× voltage
+60 dB	1000×	10⁶×	1000× voltage

Understanding decibels

When to use this: Use this to convert between decibels and voltage or power ratios — for filter design, amplifier gain calculations, audio signal levels, and RF system link budgets. The reference table below is useful for instant mental math without entering values.

Decibels exist because our ears and many measurement instruments respond logarithmically, not linearly. A 10× increase in power sounds roughly 'twice as loud', not ten times louder. Using dB compresses wide ratios into manageable numbers: a 1,000,000:1 power ratio becomes just 60dB. An amplifier with 1,000,000× voltage gain is a '120dB amplifier'. Both are easier to work with.

There are two dB formulas and mixing them up is a common mistake. For power ratios: dB = 10 × log₁₀(P₂/P₁). For voltage or amplitude ratios: dB = 20 × log₁₀(V₂/V₁). The factor of 2 difference comes from the fact that power is proportional to voltage squared (P = V²/R). Both formulas give the same dB value for the same underlying power change.

This is why −3dB means two different things depending on what you're measuring. In power: −3dB is half the power (×0.5). In voltage: −3dB is 70.7% of the amplitude (×1/√2 ≈ 0.707). Filter cutoff frequencies are defined at −3dB because that's where output power drops to half — a natural engineering threshold.

The dBm scale pins a specific power level: 0dBm = 1mW. From there, +10dBm = 10mW, +20dBm = 100mW, +30dBm = 1W, −30dBm = 1µW. RF engineers use dBm to describe everything from transmitter output (+20 to +40dBm) to received signal levels (−70 to −100dBm). A signal 40dB below the noise floor is essentially undetectable.

A few values worth memorizing: +3dB doubles the power, +6dB doubles the voltage, +10dB multiplies power by 10, +20dB multiplies voltage by 10. Going negative reverses all of these. Filter spec sheets often state attenuation in dB: a −60dB stopband means the blocked signal is 1000× smaller in voltage. These numbers quickly become second nature.

Key Reference Points

−3 dB ≈ half power, 70.7% of voltage
−6 dB ≈ half voltage, 25% of power
−20 dB = ÷10 voltage, ÷100 power
+6 dB ≈ ×2 voltage, ×4 power
+20 dB = ×10 voltage, ×100 power
0 dB = unity (no gain or loss)

Practical Examples

Filter −3 dB cutoff point

The standard cutoff frequency of any filter — output is at half power and 70.7% of input voltage.

Voltage ratio: 0.707×, Power ratio: 0.5×

Attenuator −20 dB pad

A −20 dB attenuator reduces signal amplitude by exactly 10× — essential in RF and measurement setups.

Voltage ratio: 0.1×, Power ratio: 0.01×

Amplifier gain +6 dB

+6 dB is the gain of a simple non-inverting op-amp with equal feedback and input resistors (gain = 2).

Voltage ratio: 2.0×, Power ratio: 4.0×

Absolute dB scales: dBm, dBV, dBu

Regular dB expresses a ratio. Absolute dB scales pin one end of that ratio to a defined reference level:

Scale	Reference	Used in	Example
dBm	1 milliwatt (into 50Ω or 600Ω)	RF, telecom, wireless	+30dBm = 1W transmitter; −100dBm = weak received signal
dBW	1 watt	Broadcast, radar	+10dBW = 10W; 0dBW = 1W = 30dBm
dBV	1 V RMS	Audio, electronics	0dBV = 1V RMS; −20dBV = 100mV RMS
dBu	0.775 V RMS (1mW into 600Ω)	Professional audio	+4dBu = line level; −10dBu = consumer line level
dBFS	Full-scale digital	Digital audio (DAW, ADC)	0dBFS = maximum sample value; −6dBFS = half amplitude
dBi	Isotropic antenna	Antenna gain	+6dBi antenna doubles power vs isotropic in that direction

Converting between scales requires knowing the impedance. At 50Ω: 0dBm = 224mV RMS = −13dBV ≈ −10.8dBu. At 600Ω: 0dBm = 775mV RMS = 0dBu = −2.2dBV.

Quick dB mental math

A few values are worth memorizing to do instant estimation without a calculator:

Change	Power	Voltage	How to remember
+3dB	×2	×1.41	Double power = 3dB
+6dB	×4	×2	Double voltage = 6dB
+10dB	×10	×3.16	One order of magnitude in power
+20dB	×100	×10	One order of magnitude in voltage
−3dB	÷2	×0.707	Filter cutoff point
−6dB	÷4	×0.5	Half voltage
−20dB	÷100	÷10	10× attenuator
−60dB	÷10⁶	÷1000	Filter stopband rejection (typical)

These are additive: a +20dB amplifier followed by a −6dB attenuator gives a net +14dB. A +33dB system has +20dB + +10dB + +3dB = ×10 voltage × ×√10 × ×√2 ≈ ×45 voltage gain.

Formula Reference

Decibel (dB) conversion formulas

Power ratio:   dB = 10 × log₁₀(P2/P1)
Voltage ratio: dB = 20 × log₁₀(V2/V1)
Current ratio: dB = 20 × log₁₀(I2/I1)

Inverse:
P2/P1 = 10^(dB/10)
V2/V1 = 10^(dB/20)

Reference levels:
dBm:  0 dBm = 1mW into 50Ω → V = 0.224V rms
dBV:  0 dBV = 1V rms
dBu:  0 dBu = 0.775V rms (600Ω reference, audio)
dBFS: 0 dBFS = full scale digital

Additional Examples

Op-amp gain: Av=100 → how many dB?

dB = 20 × log₁₀(100) = 20 × 2 = 40 dB. This is a common gain for sensor amplifiers and audio preamps.

Gain: 40 dB

Filter attenuation at –3dB cutoff

At f₀ of an RC filter: Vout/Vin = 1/√2 = 0.707 → 20×log(0.707) = –3.01dB. Power is halved: 10×log(0.5) = –3.01dB. This defines the –3dB bandwidth.

Voltage ratio: 0.707× · Power ratio: 0.5×

Design tip

–3dB = half power = 0.707× voltage — memorize this.
Every doubling of distance: –6dB (free space), –3 to –6dB (indoor RF).
Audio: human ear perceives +10dB as 'twice as loud' (logarithmic perception).
RF: every 3dB of antenna gain doubles the effective radiated power.

Did you know? The decibel was named after Alexander Graham Bell. A 3 dB increase in power corresponds to doubling the power, while a 10 dB increase is a 10× power increase. The human ear perceives a 10 dB increase as roughly twice as loud.