Acoustic pressure from intensity calculator

Enter intensity in watts per square metre, medium density in kilograms per cubic metre, and sound speed in metres per second. The result is pressure in pascals, together with the medium's specific acoustic impedance and the values used. It is useful for engineering checks when intensity is known but an RMS pressure value is needed, provided the plane-wave assumptions are appropriate.

Understand the plane-wave relationship

For a progressive plane wave in a lossless medium, time-averaged acoustic intensity and root mean square pressure are related by I = p_rms²/(ρc). Rearranging gives p_rms = √(Iρc), which is the equation used here. The product ρc is the medium's specific acoustic impedance: it describes how pressure and particle velocity are coupled as the wave travels. Intensity must be supplied in watts per square metre, density in kilograms per cubic metre, and sound speed in metres per second to obtain pressure in pascals. The calculator also returns acoustic impedance in pascal-seconds per metre so the intermediate physical quantity remains visible and easy to audit. Intensity may be zero, producing zero pressure, while density and sound speed must be strictly positive. Every value must be finite. The computation uses the entered values directly and does not silently substitute standard air properties, because temperature, gas composition, altitude, liquids, and solids can all change density or propagation speed enough to matter in a technical calculation.

Choose inputs that match the measurement

Use time-averaged intensity for the same wave and location represented by the desired RMS pressure. Do not enter sound power without first dividing it by an appropriate propagation area, because watts and watts per square metre are different physical quantities. Likewise, use the density and sound speed of the actual medium under the relevant conditions. For ordinary room-temperature air, handbook values can support an estimate, but a calibrated result should use environmental or measured properties consistent with the test. Density and sound speed must also describe the same medium; combining air density with the speed of sound in water produces a mathematically valid number with no useful physical meaning. This relation concerns RMS pressure, not peak pressure or peak-to-peak pressure. For a sinusoid, peak pressure is RMS pressure multiplied by the square root of two, but that conversion is not generally sufficient to characterize arbitrary waveforms. Keep all inputs in the stated SI units. If source data uses milliwatts per square metre, grams per cubic centimetre, or another unit system, convert it before calculation so that the returned pressure is correctly expressed in pascals.

Know when the model applies

The plane-wave equation is most appropriate where the sound field behaves locally like a single progressive wave and pressure and particle velocity are in phase. Examples include idealized propagation in a uniform duct, measurements sufficiently far from a source in a free field, and controlled acoustic experiments designed around traveling waves. It can become inaccurate in a reactive near field, a strongly reverberant room, or a standing-wave region, where energy may move back and forth and local pressure does not map to net intensity through the simple impedance ρc. Reflections, absorption, boundaries, evanescent fields, and multimode propagation can also require complex acoustic impedance or a more complete field model. Treat the result as a model-based conversion, not as a replacement for a microphone calibration or direct pressure measurement. A useful engineering workflow is to record the intensity method, medium properties, environmental conditions, and distance from the source alongside the result. That context makes later comparisons meaningful and helps reviewers decide whether the progressive plane-wave assumption was justified for the measurement geometry and frequency range.