Sound Level Converter — decibels, pascals, watts per m²

The sound level converter above translates between decibel levels and the linear physical quantities behind them: sound pressure in pascals, sound intensity in watts per square metre, and sound power in watts. A decibel is not a unit of sound in the way a metre is a unit of length. It is a logarithmic ratio to a stated reference, and if the reference changes, the same physical sound produces a different number.

Arb Digital publishes this converter as part of a free technical reference library. It uses the standard acoustic references of 20 micropascals for pressure and one picowatt for intensity and power, and it keeps the three scales separate because they use different formulas: pressure levels use a factor of 20, energy-like quantities use a factor of 10.

What This Sound Level Converter Does

Choose a quantity and the tool loads the decibel scale for it alongside the linear units that belong with it. In pressure mode you can move between dB SPL, pascals, millipascals, micropascals, microbar and pounds per square inch. In intensity mode it covers dB, watts per square metre and its submultiples, and watts per square centimetre. In power mode it covers dB, watts, milliwatts, microwatts and picowatts.

Because the conversion is logarithmic, the tool routes every value through the linear SI quantity before converting out again, so a decibel-to-decibel conversion across references stays exact. The four supporting panels always show the decibel level, the SI linear value, a practical submultiple, and the raw ratio to the reference, which is the number that makes the logarithm concrete: 94 dB SPL is a pressure ratio of 50,000 to 1 against the threshold reference.

How to Use It

1. Pick the quantity. A sound level meter reading is sound pressure level. A machine specification sheet quoting a fixed emission figure is usually sound power level.
2. Enter the value in whichever direction you have it. Enter 94 and convert dB to pascals, or enter 1 pascal and convert back to dB.
3. Choose the from and to units. Decibel entries appear alongside linear ones, and the tool applies the correct 10 or 20 multiplier automatically.
4. Set the number of identical sources to see how the level changes when several equally loud machines run together, which is where linear intuition fails hardest.
5. Read the four panels for the level, the SI value, a submultiple and the ratio to reference, then use Swap to check the inverse.

The Formula and How It Is Calculated

Sound pressure level is defined as L_p = 20 log₁₀(p ÷ p₀), where p₀ is 20 micropascals. Sound intensity and sound power levels use L = 10 log₁₀(X ÷ X₀), with a reference of one picowatt per square metre for intensity and one picowatt for power.

The two different multipliers are not an inconsistency. The bel is fundamentally a ratio of powers, so a factor of 10 is the underlying definition. Sound pressure is an amplitude quantity, and acoustic intensity is proportional to pressure squared, so squaring the ratio inside the logarithm is the same as doubling the multiplier outside it. That is where the 20 comes from. Reverse the definition and you get the inverse conversions this tool uses: p = p₀ × 10^L/20 and I = I₀ × 10^L/10. The BIPM SI Brochure treats the bel, decibel and neper as units for logarithmic ratio quantities, and NIST Special Publication 811 gives guidance on stating the reference alongside the value.

Why Decibels Do Not Add

This is the rule that catches everyone. Two machines each producing 80 dB do not produce 160 dB. They do not produce 85 dB either. They produce approximately 83 dB.

The reason is that decibels are logarithms of energy ratios, and energy adds linearly while the logarithm does not. Two equal, uncorrelated sources double the acoustic energy, and 10 log₁₀(2) is 3.01, so the level rises by about 3 dB. Four identical sources are four times the energy and 6 dB up. Ten identical sources are 10 dB up. The rule generalises to ΔL = 10 log₁₀(n) for n identical sources.

Combining unequal levels follows the same principle but needs the full sum: convert each level back to its linear energy, add them, and take the logarithm of the total. A useful shortcut falls out of this. When two levels differ by 10 dB or more, the quieter one contributes less than half a decibel to the total and can usually be ignored. Adding a 70 dB source to an 85 dB environment changes almost nothing measurable, which is why treating a small noise source in a loud room is rarely the effective first move.

Distance, the Inverse Square Law, and the 6 dB Rule

For a point source radiating freely, intensity falls with the square of distance, so the level drops by 6 dB for every doubling of distance. Move from 1 metre to 2 metres and you lose 6 dB; move to 4 metres and you have lost 12 dB in total.

That rule has real limits. It assumes free-field conditions with no reflecting surfaces, and it assumes a source small compared to the distance. A long line source such as a busy road behaves differently, dropping only about 3 dB per doubling of distance, because the geometry spreads energy over a cylinder rather than a sphere. Indoors, once you are beyond the critical distance where reverberant energy dominates direct energy, the level stops falling with distance almost entirely. This is why a measurement position must always be recorded with a level, and why comparing two noise figures taken at unstated distances is meaningless. Distances can be converted in the length converter.

Sound Power Versus Sound Pressure

Sound power is a property of the source alone: how much acoustic energy per second it emits, measured in watts and levelled against one picowatt. Sound pressure is a property of a location: what the air is doing at the point where the microphone sits. Sound power does not change when you move the microphone. Sound pressure does.

Equipment manufacturers publish sound power levels because they are room-independent and therefore comparable between products, and those figures are typically 5 to 15 dB higher than the pressure level you will measure a metre away, which regularly surprises people reading a specification sheet. Regulatory noise limits, by contrast, are usually written as pressure levels at a stated position, because that is what a person is exposed to. Converting between them requires knowing the radiating area and the acoustic environment, so a datasheet power level cannot simply be read as a pressure level. The underlying watts convert in the power converter.

Weighting Curves Are Not a Fixed Offset

Levels are frequently reported as dB(A) or dB(C). These are not different units. They are the same decibel scale after the signal has been passed through a standardised frequency filter that approximates how human hearing responds unevenly across the spectrum. A-weighting rolls off low frequencies heavily; C-weighting is much flatter and is used for peak and low-frequency assessment.

Because the filter is frequency dependent, there is no single number that converts unweighted dB to dB(A). At 1 kHz the A-weighting is 0 dB by definition. At 100 Hz it is about 19 dB down, and at 31.5 Hz around 39 dB down. A machine whose noise is dominated by low-frequency rumble can read dramatically lower in dB(A) than in unweighted or C-weighted terms, while a hiss-dominated source may barely change. Any tool offering a fixed dB to dB(A) conversion is fabricating a factor, which is why this converter does not offer one. Spectral work belongs alongside the frequency converter. Occupational context and measurement conventions are covered by the NIOSH noise and hearing loss resource.

Sound Level Reference Table

Sound pressure level against absolute pressure, using the standard reference of 20 micropascals:

Linear units supported, with their value in the SI unit for each quantity:

Common Mistakes to Avoid

• Adding decibel levels arithmetically — two 80 dB sources give about 83 dB, not 160 dB, because the logarithm sits on top of energy that adds linearly.
• Using a factor of 10 for pressure levels — sound pressure is an amplitude quantity and needs a factor of 20; only intensity and power use 10.
• Quoting a level with no reference or no distance — a decibel figure without both is not a physical measurement and cannot be compared.
• Converting dB to dB(A) with a fixed offset — the weighting is frequency dependent, ranging from 0 dB at 1 kHz to nearly 40 dB of attenuation at 31.5 Hz.
• Reading a machine sound power figure as the pressure you will measure — power levels are room-independent and typically run well above the pressure level at a metre.

Related Free Tools From Arb Digital

Acoustic work touches several other unit families. Convert acoustic pressure alongside static pressure in the pressure converter, radiated power in the power converter, spectral content in the frequency converter, measurement distances in the length converter, and exposure durations in the time converter. Very small linear values read more easily through the scientific notation converter, and the general unit converter covers the rest.

Frequently Asked Questions

This tool converts acoustic units only. It is not a noise exposure assessment and must not be used to judge hearing safety or regulatory compliance, which require calibrated measurement under the applicable standard.