Sound Pressure Level

Calculator and formulas for calculating sound pressure level in dB and Pascal

Sound Pressure Level Calculator

Sound pressure level conversion

Converts between decibels (dB) and Pascal (Pa). The reference value for sound in air is 20 µPa (corresponds to 0 dB), which approximately equals the human hearing threshold at 1 kHz.

dB
Reference value: 20 µPa = 0 dB (hearing threshold)
Result
Decibels:
Pascal:

Example Calculation

Example: Normal conversation
Problem:

A normal conversation produces a sound pressure level of 60 dB. What is the corresponding sound pressure in Pascal?

Given:
  • Sound pressure level L_p = 60 dB
  • Reference value p₀ = 20 µPa = 20 × 10⁻⁶ Pa
  • Find: Sound pressure p in Pascal
Solution:

Formula for conversion dB → Pa:

\[p = p_0 \times 10^{\frac{L_p}{20}}\]

Substituting values:

\[p = 20 \times 10^{-6} \times 10^{\frac{60}{20}}\]
\[p = 20 \times 10^{-6} \times 10^3\]
\[p = 20 \times 10^{-3} = 0.02 \text{ Pa}\]
Typical sound pressure levels
Hearing threshold: 0 dB (20 µPa)
Whisper: 20-30 dB (200-630 µPa)
Conversation: 60 dB (20 mPa)
Pain threshold: 120 dB (20 Pa)
Logarithmic scale

Important: The decibel scale is logarithmic. An increase of 20 dB corresponds to a ten-fold increase in sound pressure. 60 dB is therefore 1000 times louder than 0 dB!

Formulas for sound pressure level

The sound pressure level is measured in decibels (dB) and is based on the logarithmic ratio to the reference value of 20 µPa, which approximately corresponds to the human hearing threshold at 1 kHz.

Pascal → Decibels

Conversion from sound pressure to sound pressure level.

\[L_p = 20 \times \log_{10}\left(\frac{p}{p_0}\right)\]
L_p = Sound pressure level [dB]
p = Sound pressure [Pa]
p₀ = Reference value = 20 µPa
Decibels → Pascal

Conversion from sound pressure level to sound pressure.

\[p = p_0 \times 10^{\frac{L_p}{20}}\]
Inversion of the logarithmic relationship through exponentiation.
Reference value

The reference value for sound in air.

\[p_0 = 20 \text{ µPa} = 2 \times 10^{-5} \text{ Pa}\]
Corresponds to the hearing threshold at 1 kHz (0 dB).
Level addition

Addition of sound pressure levels (not simply arithmetic).

\[L_{total} = 10 \times \log_{10}\left(\sum 10^{\frac{L_i}{10}}\right)\]
For adding multiple sound sources.
Typical sound pressure levels and corresponding sound pressures
0 dB: 20 µPa (hearing threshold)
20 dB: 200 µPa (rustling leaves)
40 dB: 2 mPa (library)
60 dB: 20 mPa (conversation)
80 dB: 200 mPa (street traffic)
100 dB: 2 Pa (pneumatic hammer)
120 dB: 20 Pa (pain threshold)
140 dB: 200 Pa (jet engine)

Detailed description of sound pressure level

Physical Fundamentals

The sound pressure level is a logarithmic measure of the strength of sound waves. Since human hearing has an enormous dynamic range (from 20 µPa to 20 Pa), a logarithmic scale is used to make these values manageable.

The decibel scale is based on the ratio to the reference value of 20 µPa, which approximately corresponds to the hearing threshold.

Usage Instructions

Select with the radio buttons whether dB or Pa should be calculated. Enter the known value and click "Calculate".

Application Areas

Acoustics and Measurement Technology

Sound level measurements, noise protection, room acoustics. Foundation for all acoustic measurements.

Occupational Safety

Noise protection regulations, hearing protection requirements. Assessment of workplace noise.

Audio Engineering

Sound engineering, loudspeaker design, recording technology. Optimization of audio systems.

Understanding hearing perception

The human ear can perceive sound pressures over an enormous range. The logarithmic decibel scale reflects the perception of the ear:

Hearing threshold (0 dB)

20 µPa - Weakest perceptible sound
Corresponds to the reference value for measurements

Comfort range (40-70 dB)

2-63 mPa - Normal environmental sounds
Library to conversation

Pain threshold (120 dB)

20 Pa - Painful sound
Hearing damage possible

Memory aid: +20 dB = 10-fold sound pressure, +6 dB = double sound pressure. The perceived loudness doubles approximately every 10 dB.


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