Decibel Calculator - dB Conversion for Voltage, Power, SPL & dBm

How to use this tool

Select voltage ratio, power ratio, SPL, or absolute power mode.
Enter a ratio, pressure, power in watts, or an absolute dBm/dBW level to see its conversion.

Common dB Reference Levels

dB SPL	Sound
0	Threshold of hearing
30	Quiet library
60	Normal conversation
85	Heavy traffic (safe limit ~8h)
110	Rock concert
120	Threshold of pain
140	Jet engine at 30 m

How dB is calculated

Decibels are a logarithmic scale, not linear. For sound pressure level (SPL), the formula is:

dB SPL = 20 × log₁₀(P₁ / P₀)

P₁: Measured sound pressure (pascals)
P₀: Reference pressure = 20 µPa (micropascals), the threshold of human hearing

Why logarithmic? Human hearing perceives sound intensity logarithmically. A 10 dB increase is often perceived as roughly "twice as loud." Physically, it represents 10× the acoustic intensity (power) and about √10, or 3.16×, the sound pressure. The log scale compresses the enormous range of human hearing (~1 trillion:1 in intensity) into a manageable 0–140 dB scale.

Relative vs. absolute dB scales

"dB" alone is always relative-a ratio with no absolute value. The suffix specifies the reference:

dB SPL: Sound pressure level, reference = 20 µPa. Used for acoustics and hearing.
dBm: Power relative to 1 milliwatt. Used in RF (radio frequency) and telecommunications.
dBW: Power relative to 1 watt. dBm is 30 dB above dBW for the same power.
dBu: Voltage relative to 0.775 V RMS. Used in professional audio.
dBFS: Decibels relative to digital full scale. 0 dBFS = maximum digital level; all other values are negative. Used in digital audio.

The absolute power mode converts watts to dBm with 10 × log₁₀(P / 1 mW), and to dBW with 10 × log₁₀(P / 1 W). In reverse, P(W) = 10^{dBW / 10}; equivalently, dBm = dBW + 30 because one watt is 1,000 milliwatts. These conversions need a power value: converting voltage to power also requires the load impedance, which this calculator does not assume.

Hearing damage thresholds (NIOSH guidelines)

85 dB SPL is the threshold for occupational hearing protection. NIOSH recommends:

85 dB: Safe for 8 hours per day.
Every 3 dB increase halves the safe exposure time. Examples:
- 88 dB: 4 hours safe
- 91 dB: 2 hours safe
- 94 dB: 1 hour safe
- 100 dB: 15 minutes safe (rock concert level)
- 115 dB: ~30 seconds safe (chainsaw, ambulance siren at close range)
120 dB: Threshold of pain. Immediate risk of hearing damage.

Permanent hearing loss is cumulative and irreversible. Use hearing protection (earplugs, earmuffs) in loud environments.

Frequently asked questions

What is the difference between voltage dB and power dB?

Voltage dB uses 20×log₁₀(ratio) and power dB uses 10×log₁₀(ratio). A voltage ratio of 2 is about +6 dB; a power ratio of 2 is about +3 dB.

What is 0 dB SPL?

0 dB SPL corresponds to the threshold of human hearing: a sound pressure of 20 µPa.

How do I convert watts to dBm or dBW?

dBm = 10×log₁₀(power in watts / 0.001 W), and dBW = 10×log₁₀(power in watts / 1 W). dBm is always 30 dB above dBW for the same power; 0 dBm is 1 mW and 0 dBW is 1 W.