Decibel Calculator: Power and Voltage Ratios in dB, Sound Pressure Level and Adding Sound Levels

Decibels for electronics, audio and noise, with the working.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose the kind of conversion.

Enter the two values, or the sound pressure, or the levels to add, or the decibels to convert.

The calculator gives the answer in dB or as ratios.

Formulas used

  • dB = 10\log_{10}\frac{P_2}{P_1}
  • dB = 20\log_{10}\frac{V_2}{V_1}
  • L_p = 20\log_{10}\frac{p}{20\,\mu\mathrm{Pa}}
  • L_{total} = 10\log_{10}\sum10^{L_i/10}

Worked example

With the default numbers in the calculator above:

  1. The ratio of the final value to the starting value: 100
  2. The change in decibels: 20 dB
  3. The voltage (or current) ratio that gives the same decibels, across the same resistance: 10

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want? A voltage, current or pressure ratio in decibels (20 log); The new or final value 10.

  1. The ratio of the final value to the starting value: 10
  2. The change in decibels: 20 dB
  3. The power ratio that goes with it, across the same resistance: 100

Common questions

How do I convert a power ratio to decibels?

Take the log to base 10 of the ratio and multiply by 10. A ratio of 100 is 20 dB.

Why is it 20 log for voltage?

Power goes with the square of the voltage, and the log of a square is twice the log, so the factor becomes 20.

How do I add two sound levels?

Convert each to energy with 10 to the power of the level over 10, add them, and convert back. Two equal sources add 3 dB.

What is 3 dB?

A doubling or halving of power.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics, acoustics or electronics text (decibels).

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