Decibel Calculator — Sound Level and Intensity
Convert between decibels, intensity, and pressure ratios. Calculate sound level changes, combine multiple sources, and understand the logarithmic dB scale.
The decibel scale is logarithmic because human hearing is. Our ears can handle an enormous range of intensities — from the faintest rustle of leaves to a jet engine — but we perceive loudness roughly logarithmically. That's why doubling sound intensity only adds 3 dB, while adding 10 dB feels about twice as loud to our ears. These two facts confuse most people, so let's unpack them.
The CalcHub decibel calculator converts between dB levels, intensity ratios, and pressure ratios.
The Formulas
Sound intensity level: L = 10 × log₁₀(I / I₀) Sound pressure level: L = 20 × log₁₀(P / P₀)- L = sound level (dB)
- I = sound intensity (W/m²)
- I₀ = reference intensity = 10⁻¹² W/m² (threshold of hearing)
- P = sound pressure (Pa)
- P₀ = reference pressure = 20 μPa
Common Sound Levels
| Source | dB |
|---|---|
| Threshold of hearing | 0 dB |
| Quiet library | 30 dB |
| Normal conversation | 60 dB |
| Heavy traffic | 85 dB |
| Rock concert | 110–120 dB |
| Jet engine at 30 m | 140 dB |
| Pain threshold | ~130–140 dB |
The Critical Numbers to Remember
- +3 dB = intensity doubles
- −3 dB = intensity halves
- +10 dB = perceived loudness doubles
- +20 dB = pressure ratio × 10 (intensity × 100)
Worked Example
A machine produces 70 dB. You add a second identical machine. What's the combined level?
Adding two equal sources: intensity doubles, so level = 70 + 10 × log₁₀(2) = 70 + 3 = 73 dB
Not 140 dB — a common misconception. You'd need 10 machines to reach 80 dB.
Why does doubling distance reduce sound by 6 dB?
Sound spreads out spherically from a point source. Doubling distance quadruples the area the sound spreads over, reducing intensity to 1/4. A factor of 4 in intensity = 10 × log₁₀(0.25) = −6 dB. This is the inverse square law applied to sound.
What dB level causes hearing damage?
Sustained exposure above 85 dB causes gradual, permanent hearing damage. OSHA limits occupational exposure to 90 dB for 8 hours, with halving the allowed time for every 5 dB increase. Rock concerts routinely expose audiences to 110+ dB.
How do noise-canceling headphones work?
Active noise cancellation samples incoming sound, generates an inverted (antiphase) waveform, and plays it through the headphone driver. The two waves interfere destructively, reducing amplitude. It works best for steady low-frequency noise (engine hum, airplane noise) and is less effective for sudden, high-frequency sounds.