Calculator
Example data table
Reference values shown for typical air measurements.
| Scenario | Input Type | Sample Inputs | Typical Output |
|---|---|---|---|
| Quiet room | SPL | p = 0.002 Pa, p₀ = 2e-5 Pa | ≈ 40 dB |
| Conversation | Intensity | I = 1e-6 W/m², I₀ = 1e-12 W/m² | ≈ 60 dB |
| Power gain | Power ratio | P₁ = 100, P₂ = 10 | 10 dB |
| Amplitude gain | Amplitude ratio | A₁ = 2, A₂ = 1 | 6.02 dB |
Formula used
- Sound Pressure Level (SPL): dB = 20 · log10(p / p₀)
- Sound Intensity Level: dB = 10 · log10(I / I₀)
- Power ratio: dB = 10 · log10(P₁ / P₂)
- Amplitude ratio: dB = 20 · log10(A₁ / A₂)
All logarithms are base 10. Inputs must be positive to avoid invalid logs.
How to use this calculator
- Select the calculation type that matches your measurement.
- Enter measured values and adjust reference values if needed.
- Pick decimals and rounding for reporting preferences.
- Press Calculate to view results above this form.
- Use CSV or PDF buttons to export the result table.
FAQs
1) Why are there 10 and 20 multipliers in decibels?
Power scales with the square of amplitude, so power ratios use 10·log10(). Amplitude ratios use 20·log10() to match equivalent power changes under similar conditions.
2) What reference pressure is commonly used in air?
A standard reference is 20 micro‑pascals (20 µPa), representing the approximate threshold of human hearing around 1 kHz in a quiet environment.
3) What reference intensity is commonly used in air?
A typical reference is 1×10⁻¹² W/m². It aligns with the same hearing threshold assumption used with the 20 µPa pressure reference.
4) Can decibel values be negative?
Yes. Negative values mean the measured quantity is below the chosen reference. This is common in very quiet conditions or when comparing two signals where the first is smaller.
5) What does a 3 dB change mean?
A +3 dB change is about a doubling of power. For amplitude, it is about a 1.414× increase. Small dB shifts can still represent meaningful physical changes.
6) What does a 10 dB change mean?
A +10 dB change equals ten times the power. For amplitude, it is about 3.162×. In perceived loudness, 10 dB is often described as roughly “twice as loud.”
7) Why must inputs be positive?
Decibels use a logarithm of a ratio. Logarithms require positive arguments, so any zero or negative measurement would make the computation undefined in real numbers.
8) Which mode should I use for microphones and speakers?
If you measure pressure, use SPL. If you have intensity, use intensity level. For amplifier or filter gain, use amplitude or power ratio based on what you measured.