Sound Pressure Level Calculator Formula

Understand the math behind the sound pressure level calculator. Each variable explained with a worked example.

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Formulas Used

Sound Pressure Level

spl = 20 * log10(pressure / 0.00002)

Variables

VariableDescriptionDefault
pressureRMS Sound Pressure(Pa)1

How It Works

Sound Pressure Level (SPL)

SPL quantifies the RMS sound pressure relative to the threshold of hearing on a logarithmic scale.

Formula

SPL = 20 * log10(p / p_0)

where p_0 = 20 micro-Pa = 2 x 10^-5 Pa is the reference pressure corresponding to the threshold of human hearing at 1 kHz.

Worked Example

A sound wave with RMS pressure of 1 Pa.

pressure = 1
  1. 01SPL = 20 * log10(p / p_0)
  2. 02SPL = 20 * log10(1 / 0.00002)
  3. 03SPL = 20 * log10(50000)
  4. 04SPL = 20 * 4.699 = 94.0 dB SPL

Frequently Asked Questions

What is the reference pressure p0?

20 micro-pascals (2 x 10^-5 Pa), chosen to match the approximate threshold of human hearing at 1 kHz.

How does SPL relate to sound intensity level?

Both use dB but SPL uses pressure (20 * log10) while intensity level uses power (10 * log10). They yield the same numeric value under standard conditions.

What is a typical SPL for conversation?

Normal conversation at 1 meter is about 60 to 70 dB SPL.

Ready to run the numbers?

Open Sound Pressure Level Calculator