SPL from Pressure
SPL = 20 × log₁₀(p / p_ref)
Quick answer
This calculator solves SPL = 20 × log₁₀(p / 20 µPa) for Sound Pressure Level. With Sound Pressure 10000 Pa, the result is 174 dB. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Sound pressure level in decibels is defined relative to the threshold of human hearing at 20 micropascals (20 µPa). This reference was chosen because it represents the quietest sound a healthy young person can perceive at 1 kHz. The logarithmic scale compresses the enormous range of pressures the ear can handle: from the threshold of hearing (0 dB SPL, 20 µPa) to the threshold of pain (130 dB SPL, about 63 Pa), a ratio of over 3 million to one in pressure. Each 20 dB increase represents a 10× increase in sound pressure.
Variables
- SPL — Sound pressure level (dB SPL)
- p — RMS sound pressure (Pa)
Practical Notes
Normal conversation is about 60-65 dB SPL (0.02 Pa), a lawnmower at 1 meter is about 90 dB SPL (0.63 Pa), and a jet engine at 30 meters is about 140 dB SPL (200 Pa). Occupational noise exposure limits are typically 85 dB SPL for 8 hours. A-weighting (dBA) applies a frequency-dependent correction to match human hearing sensitivity.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| SPL | Sound Pressure Level | dB | dB |
| p | Sound Pressure | Pa | — |
Step by step
- 1. What you know: Sound Pressure 10000 Pa
- 2. The relation: SPL = 20 × log₁₀(p / 20 µPa)
- 3. Substitute: p = 10000 Pa
- 4. Result: Sound Pressure Level = 174 dB
Worked examples
Minimum range
Given: Sound Pressure 10 Pa
Result: Sound Pressure Level = 114 dB
Low range
Given: Sound Pressure 100 Pa
Result: Sound Pressure Level = 134 dB
Typical
Given: Sound Pressure 10000 Pa
Result: Sound Pressure Level = 174 dB
High range
Given: Sound Pressure 100000 Pa
Result: Sound Pressure Level = 194 dB
Maximum range
Given: Sound Pressure 1 × 10⁶ Pa
Result: Sound Pressure Level = 214 dB
Solving for each variable
Solve for Sound Pressure Level
Sound Pressure 10 Pa → 114 dB
Solve for Sound Pressure
Sound Pressure Level 0.3 dB → 2.07 × 10⁻⁵ Pa
How Sound Pressure Level changes with Sound Pressure
| Sound Pressure (input) | Sound Pressure Level (result) |
|---|---|
| 1000 Pa | 154 dB |
| 2500 Pa | 161.9 dB |
| 5000 Pa | 168 dB |
| 7500 Pa | 171.5 dB |
| 10000 Pa | 174 dB |
| 15000 Pa | 177.5 dB |
| 20000 Pa | 180 dB |
| 40000 Pa | 186 dB |
| 70000 Pa | 190.9 dB |
| 100000 Pa | 194 dB |
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<p><a href="https://vbatpower.com/formulas/spl-pressure/">SPL from Pressure</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate SPL from Pressure?
Use SPL = 20 × log₁₀(p / 20 µPa). With Sound Pressure 10000 Pa, Sound Pressure Level works out to 174 dB.
What is the formula for SPL from Pressure?
The formula is SPL = 20 × log₁₀(p / 20 µPa). Sound pressure level in decibels is defined relative to the threshold of human hearing at 20 micropascals (20 µPa).
How do you find Sound Pressure when you know the other values?
Rearrange for Sound Pressure: with Sound Pressure Level 0.3 dB, Sound Pressure is 2.07 × 10⁻⁵ Pa.
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