dB To Normal Value

A level change of 3 dB means the normal value of the power doubles.

The dB to normal value formula

The normal value of a power change equals 10 to the power of dB divided by 10.

For voltage the divisor is 20.

Take 13 dB. 10^(13 ÷ 10) gives 19.953.

Take 26 dB. 10^(26 ÷ 10) gives 398.11.

The plain number behind the dB

A dB figure is a ratio on a log scale. The normal value is that ratio as an everyday number of times, such as 2 times or 0.1 times (Engineering ToolBox: Decibel).

It is easier to picture a power that doubles than a power that rises by 3 dB.

How to convert dB to normal value step by step

1. Read the dB figure.
2. Divide by 10 for a power change, or by 20 for a voltage change.
3. Raise 10 to that power.
4. Read how many times bigger or smaller the value is.

The three examples below use common sizes.

Each one shows the sum in full.

dB to normal value conversion table

The highlighted row is the default of the calculator. The last column gives voltage.

A quick mental shortcut for dB to normal value

Use the 10 plus 3 trick. Split the dB into tens and threes, then multiply. 13 dB is 10 plus 3, so 10 times 2, which is about 20.

26 dB is 10 plus 10 plus 3 plus 3, so 10 times 10 times 2 times 2, which is about 400.

Check the trick

The exact power value of 13 dB is 19.95 and of 26 dB is 398.1. The trick gives 20 and 400, which are close.

For rough work, that is good enough.

Bigger and smaller

A positive dB means the value grew, and a negative dB means it shrank. Minus 13 dB gives about 0.05 times the power, which is one twentieth.

Going down by 10 dB divides the power by 10.

Voltage in normal terms

For a voltage, 20 dB is 10 times and 6 dB is about 2 times. So 26 dB is about 20 times the voltage, from 20 plus 6.

The voltage column in the table shows the exact number.

Quick conversion answers

Where this conversion is used

Hobbyists turn a dB figure on a data sheet into a plain multiplier.

Teachers show students what a log scale hides.

Common mistakes to avoid

• Reading 3 dB as 3 times. It is about 2 times the power.
• Using the voltage rule for power. The divisor is 10 for power.
• Adding ratios. Multiply the ratios or add the dB.
• Ignoring a minus sign. It means a fall, not a rise.

Related converters

• dB to ratio
• dB to linear
• dB to percentage
• decibel calculator

More dB figures

5 dB is 3.162. 8 dB is 6.31. 11 dB is 12.59.

14 dB is 25.12. 17 dB is 50.12. 23 dB is 199.5.

33 dB is 1,995. 43 dB is 19,953. -23 dB is 0.005012.

Doubling the first number

10 dB is 10. 16 dB is 39.81. 22 dB is 158.5.

28 dB is 631. 34 dB is 2,512. 46 dB is 39,811.

66 dB is 3,981,072. 86 dB is 398,107,171. -46 dB is 0.00002512.

Tens and threes

3 dB is 1.995. 10 dB is 10. 13 dB is 19.95.

20 dB is 100. 23 dB is 199.5.

Going back to dB

To go back, take 10 times the log of the power ratio. A power ratio of 2 is about 3.01 dB, and a ratio of 10 is exactly 10 dB.

A ratio of 400 is about 26.02 dB, and a ratio of 0.05 is about minus 13.01 dB.

The trick against the exact value

At 3 dB the trick says 2 and the exact value is 1.995. At 13 dB the trick says 20 and the exact value is 19.95.

At 10 dB and 20 dB the trick is exact, at 10 and 100.

Why people use dB at all

Gains and losses on a chain simply add in dB. In plain numbers you would have to multiply every step.

The dB scale also squeezes a huge range of values into short numbers.

When the trick is not enough

For odd values such as 4 dB or 7 dB, use the table or the formula. The trick gives only a rough idea there.

Use the formula whenever the answer matters for a design.

Half and double

Each 3 dB step doubles or halves the power. Three steps up is 9 dB, which is about 7.94 times, and three steps down is about 0.126 times.

So the numbers stay easy to picture.

Frequently asked questions

Sources

• Engineering ToolBox: Decibel (engineeringtoolbox.com)
• Wikipedia: Decibel (en.wikipedia.org)