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Decibel calculator

A decibel is a ratio, out ÷ in, on a logarithmic scale. Gain is positive, loss is negative, and 0 dB means no change. Type an output and an input to get the decibels, or type decibels to get the ratio back, for voltage or for power.

Voltage out

Or type a ratio here, with 1 below.

Voltage in

Any unit, as long as both match.

Gain, 20 × log₁₀(out ÷ in)

−20 dB

Ratio, out ÷ in: 0.1
Power ratio, the same dB: 0.01
So it's: a loss

The formulas

dB = 20 × log₁₀(V_out ÷ V_in) dB = 10 × log₁₀(P_out ÷ P_in)

Power goes with voltage squared, so both give the same number of decibels for the same change, measured across the same resistance. Back the other way:

voltage ratio = 10^{dB ÷ 20} power ratio = 10^{dB ÷ 10}

Voltage ratio	Power ratio	Decibels
0.01	0.0001	−40 dB
0.1	0.01	−20 dB
0.5	0.25	−6 dB
0.707	0.5	−3 dB
1	1	0 dB
2	4	+6 dB
10	100	+20 dB

Along a chain the ratios multiply and the decibels add: −6 dB then −14 dB is −20 dB.

A worked example

A resistor in series before a 50 Ω load is a pad: it takes a set number of decibels off a signal. To leave a tenth of the voltage:

20 × log₁₀(0.1) = −20 dB

The load gets 50 ÷ (PAD + 50) of the volts, so a tenth needs PAD = 50 × (10 − 1) = 450 Ω. The power is a hundredth: still −20 dB.

dBm and other levels

Levels like dBm are decibels against a stated reference. 0 dBm is 1 mW, +30 dBm is 1 W, and Wi-Fi signals sit around −50 to −80 dBm. To turn milliwatts into dBm here, choose power, type your power as the output and 1m as the input.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Count the decibels” is lesson 3 of 6 in Carrier Cove, Signals & Wireless (RF) World 1. Free with an account. Lessons unlock in order, so you’ll do the 2 before it first.

Or start from the very first lesson, no account needed

The ideas behind it

Questions people ask

How do you convert a voltage ratio to decibels?

dB = 20 × log₁₀(Vout ÷ Vin). Half the voltage is −6 dB, a tenth is −20 dB, and double is +6 dB. For a power ratio, use 10 × log₁₀ instead.

How do you convert decibels back to a ratio?

For voltage, the ratio is 10^(dB ÷ 20); for power, 10^(dB ÷ 10). So −20 dB is a tenth of the voltage and a hundredth of the power, and +3 dB is about twice the power.

Why do engineers use decibels?

Along a chain of cables, filters and amplifiers the ratios multiply, but decibels simply add. −6 dB, −14 dB and +20 dB make 0 dB: no change overall, worked out in your head.

What does −3 dB mean?

Half the power, which is about 70.7% of the voltage. That's why a filter's cutoff is called its −3 dB point.

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