Decibels compress enormous ranges into manageable numbers. Audio power, radio signal strength and amplifier gain all span many orders of magnitude, and expressing their ratios in decibels turns multiplication into addition: a gain of ten decibels followed by another ten is twenty decibels, regardless of the absolute levels involved. The conversion differs for power and for voltage, because power depends on the square of voltage, so power ratios use ten times the logarithm while voltage ratios use twenty times. Mixing those two factors is the classic decibel mistake. This calculator handles both directions and both quantity types, converting a ratio to decibels and a decibel figure back to a ratio, with the correct factor applied for the type you choose.
Quick Answer: Choose power or voltage, enter a ratio and click Ratio to dB, or enter decibels and click dB to Ratio for the reverse conversion.
Free Online Tool
Decibel Calculator
Ratios to decibels and back, with the correct power and voltage factors.
How to Use the Decibel Calculator
- Choose whether your ratio is a power ratio or a voltage ratio, since the factor differs.
- For a ratio conversion, enter the ratio as a plain number, such as output divided by input.
- Click Ratio to dB to see the decibel figure for that ratio.
- For the reverse, enter a decibel figure and click dB to Ratio to recover the ratio.
- Read the result with its type label, so a power decibel is never mistaken for a voltage decibel.
Key Features
- Power ratio conversion using ten times the base ten logarithm.
- Voltage ratio conversion using twenty times the base ten logarithm.
- Reverse conversion from decibels back to a plain ratio for both types.
- Gain and loss handling: ratios below one correctly produce negative decibel figures.
- Clear type labelling on every result, preventing the common factor mix up.
Best Practices and Tips
- Remember the doubling rules: doubling power is about three decibels, while doubling voltage is about six decibels.
- Add decibels along a signal chain instead of multiplying ratios, which is the main reason the scale exists.
- A negative decibel figure means loss, not an error. An attenuator that halves power shows about minus three decibels.
- State the quantity type whenever you quote decibels, since the same decibel figure means different ratios for power and voltage.
Common Mistakes to Avoid
- Using twenty log for a power ratio, or ten log for a voltage ratio, which doubles or halves the answer.
- Treating decibels as an absolute unit. Decibels always express a ratio, and an absolute level needs a reference, such as dBm or dBV.
- Adding decibel figures from different quantity types in one chain without converting them to a common basis.
Frequently Asked Questions
Why are there two formulas?
Power is proportional to voltage squared, so the logarithm of a power ratio equals twice the logarithm of the corresponding voltage ratio. The factor of ten for power and twenty for voltage both come from the same definition, applied to quantities related by that square law.
What does zero decibels mean?
Zero decibels means a ratio of one: output equals input, with neither gain nor loss. It does not mean silence or zero signal, which is a common misunderstanding caused by treating decibels as an absolute scale.
How do I convert a gain chain?
Add the decibel gains and losses of each stage in order. A plus ten decibel amplifier followed by a minus three decibel cable gives a net plus seven decibels, which corresponds to a power ratio of about five, without multiplying any ratios directly.
What is the difference between dB, dBm and dBV?
Plain dB expresses a ratio between two levels. dBm expresses power relative to one milliwatt, and dBV expresses voltage relative to one volt. The suffixed forms are absolute levels with a stated reference, while plain dB always needs two levels to be meaningful.