Decibel Calculator
Calculate dB gain, sound pressure, combined sound levels, absolute power, and free-field distance changes.
For informational use; not a calibrated sound meter or occupational exposure assessment. Terms and Conditions
Positive input and output powers; gain is output divided by input.
Select calculation
Choose the type of decibel relationship you need.
Enter known values
Example values update automatically as you edit.
Result
Calculated answer, relevant checks, and calculation steps.
Result details
Show calculation stepsFormula, substitution, units, and scope
- Enter valid values to see the complete calculation.
Method, Sources, and Assumptions
Logarithmic relationships and model limitations.
Power levels use 10 log10 of a positive power ratio; amplitude and sound pressure use 20 log10 of a positive amplitude ratio. A displayed dBA or dBC level identifies the weighting of previously weighted input measurements; this calculator does not apply frequency weighting. Acoustic combination assumes incoherent sources with identical references and weighting. Distance predictions are ideal free-field point-source estimates.
- Example values are illustrative, not measurements or compliance thresholds.
How to Calculate Decibels
A decibel (dB) describes a ratio on a logarithmic scale. For a power ratio, calculate 10 times its base-10 logarithm; for a comparable voltage-amplitude ratio, calculate 20 times its base-10 logarithm. Use the Decibel Calculator above to calculate power or voltage gain, sound pressure level, combined noise, dBm and dBW conversions, or an idealized sound-level change with distance.
A positive output-to-input gain means the output exceeds the input; a negative gain means attenuation. A level expressed as dBm or dB SPL also needs its specified reference. A numerical result is only meaningful when its physical quantity and reference are identified.
- Known values
- Two comparable quantities, a level and its reference, or the mode-specific acoustic measurements.
- Result
- A labeled gain, level, power, sound pressure, or distance.
- Scope
- Computes from entered data; it is not a microphone-based sound meter.
Select the Calculation type and, when shown, the Calculate option. Replace the example inputs and check the result label, units, and method note. Supported input units are converted without changing the underlying quantity. Open Show calculation steps for a numerical check; use the warnings and source assumptions before applying an acoustic estimate to an installation.
Power and Voltage Decibel Formulas
Power and voltage ratios use related but distinct formulas. Both compare quantities of the same type; the order of the numerator and denominator determines whether the result is gain or loss.
Power gain and reverse conversion
Divide output power by input power, take the base-10 logarithm, then multiply by 10. To recover the linear ratio, use 10 raised to the power of the gain divided by 10.
Voltage-amplitude gain and reverse conversion
Divide the output voltage magnitude by the input voltage magnitude, take the base-10 logarithm, and multiply by 20. To recover the ratio, raise 10 to the power of the voltage gain divided by 20.
- \(G_P\)
- Power gain Output-to-input power level difference.
- \(P_1, P_2\)
- Input and output powers Positive physical powers, in compatible units.
- \(G_V\)
- Voltage gain Output-to-input voltage-amplitude level difference.
- \(V_1, V_2\)
- Input and output voltage magnitudes Consistently measured RMS or peak amplitudes; the calculator’s voltage fields accept V and mV.
Why voltage gain is not always power gain
Power is proportional to the square of voltage for a fixed resistive load, which explains the factor of 20. If the loads differ, voltage gain alone cannot establish delivered power gain. For example, 1 V RMS across 50 Ω is 20 mW, while 2 V RMS across 100 Ω is 40 mW: voltage gain is +6.02 dB but the delivered-power ratio is only 2, or +3.01 dB. The current voltage mode does not calculate unequal-impedance delivered-power gain; determine each real power separately when that distinction matters.
Worked Example: A 10 W to 20 W Power Gain
Suppose an amplifier receives 10 W and delivers 20 W. Calculate the output-to-input power gain using the default Power gain / loss example above.
Substitute the values
Both powers are expressed in watts, so no conversion is necessary.
Result
+3.01 dB power gain
The output power is twice the input power. The positive sign denotes gain under the output/input convention.
How to Add and Subtract Sound Levels
Adding the numbers in two sound-level readings does not give their combined level. For independent, incoherent sources measured at the same receiver with compatible pressure references and weighting, add their relative mean-square sound-pressure contributions before converting the total back to decibels.
Combine independent sources
Convert every compatible level to 10 raised to level/10, sum those quantities, then take 10 times the logarithm of the sum.
Here, each Lᵢ is an individual source level in dB and n is the number of independent sources. Two 80 dB sources combine to 83.01 dB; an 80 dB source and a 90 dB source combine to about 90.41 dB. The calculator’s combination mode accepts two or three sound-source inputs.
Subtract background noise
Convert the measured total and background levels to linear contributions, subtract the background, then convert the positive remainder back to dB. In the equation, Lₛ is the estimated source-only level, Lₜ is the measured total, and Lᵦ is the background level.
For a measured total of 85 dB and background of 80 dB, the estimated isolated source is 83.35 dB. Measure the background under comparable operating conditions, preferably with the source of interest switched off.
Sound Pressure Level (dB SPL)
Sound pressure level compares RMS acoustic pressure with a stated reference. In air, the conventional pressure reference is 20 µPa (0.000020 Pa); underwater acoustic pressure levels commonly use 1 µPa. These are different reference conventions, not interchangeable measurements.
Calculate SPL from acoustic pressure
Divide RMS acoustic pressure by the selected reference pressure, then multiply the base-10 logarithm by 20. Here Lₚ is the sound pressure level in dB SPL; p rms is RMS acoustic pressure and p ref is the selected reference pressure, both in pascals.
For 1 Pa RMS in air, the result is approximately 93.98 dB SPL. Conversely, 94 dB SPL in air corresponds to about 1.0024 Pa RMS. Zero dB SPL corresponds to the reference pressure, not zero acoustic pressure; a pressure below the reference can yield a negative dB SPL value.
The calculator lets you choose the air or underwater reference and convert between supported pressure units (Pa, mPa, and µPa). Selecting a reference does not model underwater propagation or transform an airborne measurement into an equivalent underwater one.
Convert dBm, dBW, and Watts
A plain dB power gain compares two powers; dBm reports a power relative to 1 milliwatt, and dBW reports a power relative to 1 watt. Consequently, 0 dBm means 1 mW, whereas 0 dBW means 1 W.
Watts to dBm
Divide positive power in watts by 0.001 W, then multiply the base-10 logarithm by 10.
dBm to watts and dBW
Subtract 30 from the dBm reading, divide by 10, then raise 10 to that power. Subtracting 30 directly from a dBm value gives its dBW value.
For example, 30 dBm equals 1 W, 1,000 mW, and 0 dBW. The calculator’s absolute-power mode supports dBm, dBW, watts, and the displayed smaller power units; do not confuse antenna gain in dBi with an absolute power level in dBm.
Sound Level Change with Distance
An approximately omnidirectional point source in a free field loses about 6.02 dB of sound pressure level for each doubling of receiver distance. This is a model of the change in sound level, not a guaranteed indoor or outdoor measurement.
Free-field point-source relationship
Subtract 20 times the logarithm of new distance divided by reference distance from the known sound level. Here L₁ and L₂ are the sound levels at distances r₁ and r₂, respectively, using consistent distance units.
For an illustrative source producing 90 dB SPL at 1 m, the predicted level is 83.98 dB at 2 m, 77.96 dB at 4 m, and 71.94 dB at 8 m. The calculator can also solve for the distance required to reach a specified target level under the same idealized model.
| Receiver distance (m) | Predicted level (dB SPL) |
|---|---|
| 1 | 90.00 |
| 2 | 83.98 |
| 4 | 77.96 |
| 8 | 71.94 |
| 16 | 65.92 |
Inside a room, reflected and reverberant sound can prevent the expected 6 dB reduction. Large or distributed sources, barriers, source directionality, ground effects, and nearby surfaces can also change the result. For real installations, verify the sound level at the actual receiver or use an acoustic model suited to the source and environment.
Decibel Conversion Reference Charts
Use these mathematical reference values to check the order of magnitude of a result. The power and amplitude columns refer to different physical ratios; they should not be interchanged.
| Change (dB) | Power ratio | Amplitude ratio |
|---|---|---|
| −20 | 0.01× | 0.1× |
| −10 | 0.1× | 0.3162× |
| −6.02 | ≈0.25× | ≈0.5× |
| −3.01 | ≈0.5× | ≈0.7071× |
| 0 | 1× | 1× |
| +3.01 | ≈2× | ≈1.4142× |
| +6.02 | ≈4× | ≈2× |
| +10 | 10× | 3.1623× |
| +20 | 100× | 10× |
| +30 | 1,000× | 31.6228× |
| Level (dBm) | Watts (W) | Milliwatts (mW) |
|---|---|---|
| −30 | 0.000001 | 0.001 |
| −20 | 0.00001 | 0.01 |
| −10 | 0.0001 | 0.1 |
| 0 | 0.001 | 1 |
| +10 | 0.01 | 10 |
| +20 | 0.1 | 100 |
| +30 | 1 | 1,000 |
| +40 | 10 | 10,000 |
For n equal, independent incoherent sound sources at the same receiver, the total level exceeds one source by 10 log₁₀(n) dB: two equal sources add 3.01 dB, four add 6.02 dB, and ten add 10 dB. This is a mathematical reference rather than a claim that the current interface accepts an unlimited number of source inputs.
Acoustic Measurement and Engineering Limits
A correct calculation can still give an unsuitable engineering conclusion if the measurements, references, or real operating conditions do not match the method.
dB, dBA, dBC, and dBZ
dB identifies a logarithmic quantity; dBA and dBC identify sound levels with different frequency-weighting responses. Z-weighting is nominally flat over its specified measurement band. The calculator’s weighting choice labels compatible existing sound measurements—it does not convert an unweighted broadband number to dBA or dBC. Such a conversion generally requires frequency-resolved information.
Sound pressure vs. sound power
Sound pressure level describes the received acoustic pressure at a specific location. Sound power level describes a source’s emitted acoustic power relative to its specified reference. A manufacturer’s sound-power rating cannot simply be entered as a sound-pressure reading; room and propagation conditions matter.
Source and measurement conditions
Combine acoustic measurements only when their reference, weighting, receiver position, and operating conditions are comparable. Changes in machine speed, background noise, or measurement location can alter the actual combined level. Coherent signals may require phase-aware treatment instead of independent-source addition.
Noise exposure and equipment decisions
The calculator does not calculate a worker’s cumulative noise dose or establish occupational compliance. Real assessments need exposure time, suitable measurements, the applicable weighting and measurement procedure, and the relevant regulatory framework. A free-field result alone cannot establish compliance with an installed-equipment noise requirement.
Troubleshoot Unexpected Decibel Results
If a result looks implausible, first check the calculation type, ratio order, unit selection, and acoustic reference rather than changing the input numbers until the answer looks familiar.
Gain has the opposite sign
For an output/input comparison, reversing the ratio reverses the dB sign. Check which value represents input and which represents output.
Voltage change mistaken for power gain
Twice the voltage is +6.02 dB voltage gain; it does not establish delivered power without the applicable load conditions. Determine the relevant real powers separately when impedances differ.
Sound levels simply added
Two independent 80 dB sources combine to 83.01 dB, not 160 dB. Use logarithmic summation and compatible measurements at the same receiver.
Unexpected SPL or distance estimate
Check whether the selected pressure reference is for air or underwater sound, whether the known distance is nonzero, and whether a free-field point-source model is appropriate to the actual setting.
Technical References
The relationships on this page follow logarithmic unit definitions and conventional acoustic measurement methods. Examples are rounded after calculation; measured inputs may have greater uncertainty than the displayed result.
- NIST Guide for the Use of the International System of Units — logarithmic quantities, SI units, and their reference conventions.
- OSHA Technical Manual: Noise — sound pressure, combining sound levels, measurement conditions, and propagation considerations.
- NIOSH: Noise and Hearing Loss Prevention — occupational-noise measurement and exposure context, which this general calculator does not assess.
Decibel Calculator FAQ
Can decibels be negative?
Yes. A negative relative gain means the numerator is smaller than the reference quantity. Negative dBm represents positive physical power below 1 mW; negative dB SPL represents positive RMS sound pressure below the selected pressure reference.
Does zero dB mean silence?
No. Zero dB indicates equality with the selected reference. Zero dB SPL in air corresponds to 20 µPa RMS, whereas zero dB power gain means equal input and output powers.
Is a 10 dB change twice as loud?
A +10 dB change represents 10 times the associated physical power ratio, but perceived loudness is not a fixed conversion. Listening conditions, sound spectrum, and the listener affect the perceived change.
Why can I subtract dB values for a difference but not for background correction?
Subtracting two levels gives their level difference. Isolating one independent source from a combined measurement requires subtracting compatible linear mean-square pressure contributions, then converting the positive remainder back to dB.
Can the calculator measure sound with my microphone?
No. It processes values you enter. Measuring actual sound pressure requires an appropriate sound-level meter or calibrated measurement system.
Can I convert dBA to dB SPL from one number?
Not generally. A-weighting depends on the sound frequency distribution; one broadband A-weighted reading does not contain enough information for a general unweighted conversion.