What Is a Decibel?

The decibel (dB) is a logarithmic unit used to express the ratio between two values — most commonly sound intensity, signal power, or voltage. Rather than using unwieldy numbers, the decibel scale compresses huge ranges into manageable figures.

Core Formulas

Power Formula

dB = 10 × log₁₀(P₁/P₀)

Used for signal power, sound intensity, and energy measurements

Amplitude Formula

dB = 20 × log₁₀(V₁/V₀)

Used for voltage, sound pressure, and field quantities

Understanding the Scale: Because the scale is logarithmic, a 10 dB increase represents a 10× increase in power, while a 20 dB increase represents a 100× increase. This is why the difference between 60 dB (normal conversation) and 80 dB (busy traffic) feels much larger than just "20 units."

Why Use This Calculator?

Dual Conversion

Convert between dB values and ratios in both directions

Source Combination

Calculate combined sound levels from multiple sources

Distance Attenuation

Determine how sound decreases over distance

This calculator handles three common decibel tasks in one tool, with real-time calculations and hearing safety information based on the NIOSH standard.

How to Use the Decibel Calculator

Converter Mode

Convert between decibel values and ratios with precision:

Choose Direction

Select Ratio → dB or dB → Ratio depending on your starting value

Select Type

Choose Power (10×log₁₀) for power/intensity, or Amplitude (20×log₁₀) for voltage/pressure

Enter Value

Input your value — the result and complete formula breakdown appear instantly

Addition Mode

Calculate the combined sound level when multiple sources operate simultaneously:

Enter Sound Levels

Input the dB level for each individual sound source

Add More Sources

Click Add Source to include additional sound sources in your calculation

Use Quick Presets

Apply presets for 2 or 10 equal sources to see common scenarios instantly

Formula used: L = 10 × log₁₀(Σ10^(Lᵢ/10)) — This accounts for the logarithmic nature of decibels

Distance Mode

Determine how sound level changes as you move away from the source:

Known Sound Level

Enter the measured sound level in dB at your reference point

Reference Distance

Input the distance (d₁) where the sound level was measured

Target Distance

Enter the new distance (d₂) where you want to calculate the sound level

Inverse Square Law: L₂ = L₁ − 20 × log₁₀(d₂/d₁) — Sound level decreases approximately 6 dB when distance doubles

Sound Level Reference

Below the calculator, a color-coded bar shows where your result falls on the hearing scale — from the threshold of hearing (0 dB) to the theoretical maximum (194 dB). Levels above 85 dB trigger a warning with the safe exposure time based on NIOSH guidelines.

Features

Dual Conversion Modes

Convert in both directions — from a ratio to decibels or from decibels back to a ratio.

Power formula (10×log₁₀) for signal power and intensity
Amplitude formula (20×log₁₀) for voltage, pressure, and field quantities
Instant bidirectional conversion

Sound Source Addition

Combine any number of sound sources to find the total noise level.

Add or remove sources freely
Quick presets: 2 sources (+3 dB) or 10 sources (+10 dB)
Accurate logarithmic summation

Distance Attenuation

Calculate how sound level decreases with distance using the inverse square law.

Useful for noise control and speaker placement
Environmental acoustics applications
Free-field propagation modeling

Real-Time Calculation

Results update instantly as you type or change settings.

No submit button required
Complete formula breakdown displayed
Immediate feedback on every change

Sound Level Reference Bar

A visual gradient bar maps your result against common noise levels.

From whisper (20 dB) to fireworks (140 dB)
Color-coded: green (safe) → yellow (caution) → red (dangerous)
Instant visual context for results

Hearing Safety Warnings

Automatic safety alerts when sound levels exceed safe exposure limits.

Triggers at 85 dB and above
Maximum safe exposure time calculated
Based on NIOSH standard formula

Frequently Asked Questions

What is the difference between power dB and amplitude dB?

Power dB

10 × log₁₀(ratio)

Signal power
Sound intensity
Energy measurements

Amplitude dB

20 × log₁₀(ratio)

Voltage
Sound pressure
Electric field strength

Why the factor of 20? Power is proportional to the square of amplitude, so the amplitude formula uses 20 instead of 10 to maintain consistency.

Why does adding two 60 dB sources not equal 120 dB?

Because decibels use a logarithmic scale, not a linear one. Two identical sound sources produce a combined level that is about 3 dB higher than each individual source — so two 60 dB sources combine to roughly 63 dB, not 120 dB.

Correct formula: L = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10))

Common Combinations:

2 identical sources = +3 dB increase
4 identical sources = +6 dB increase
10 identical sources = +10 dB increase

What is the inverse square law for sound?

In free-field conditions (outdoors, no reflections), sound level decreases by approximately 6 dB each time you double the distance from the source.

Formula: L₂ = L₁ − 20 × log₁₀(d₂/d₁)

Practical Example:

At 1 meter

100 dB

At 2 meters

94 dB (−6 dB)

At 4 meters

88 dB (−12 dB)

Important note: Real environments with walls and obstacles will differ from this ideal model. The inverse square law applies best in open, outdoor spaces.

What is the NIOSH safe exposure time?

The National Institute for Occupational Safety and Health (NIOSH) recommends a maximum exposure time based on sound level. At 85 dB, the limit is 8 hours. For every 3 dB increase, the safe time is halved.

Safe Exposure Times:

Sound Level	Maximum Exposure	Common Example
85 dB	8 hours	Heavy traffic
88 dB	4 hours	Lawn mower
91 dB	2 hours	Subway train
94 dB	1 hour	Motorcycle
100 dB	15 minutes	Nightclub
106 dB	3.75 minutes	Rock concert

Formula: T = 8 / 2^((L−85)/3) hours — Prolonged exposure above these limits can cause permanent hearing damage.

Can decibel values be negative?

Yes. A negative dB value simply means the measured quantity is less than the reference level. For example, −3 dB in power terms means the signal is half the reference power.

Common Negative dB Values:

−3 dB = 50% power (half power point)
−6 dB = 50% amplitude (half voltage)
−10 dB = 10% power
−20 dB = 1% power

Common in: Electronics, signal processing, audio engineering, and telecommunications where signals are often attenuated below reference levels.

What is 194 dB?

194 dB SPL is the theoretical maximum sound pressure level in Earth's atmosphere at standard conditions. Beyond this point, the sound wave's pressure troughs would create a vacuum, meaning the wave can no longer propagate as a normal sound wave.

Why 194 dB?

At standard atmospheric pressure (101.325 kPa), a sound wave with peak pressure equal to atmospheric pressure reaches 194 dB SPL. The negative pressure phase would theoretically reach absolute vacuum.

Beyond 194 dB

Above this level, the wave becomes a shock wave rather than a sound wave. Examples include rocket launches (180+ dB) and volcanic eruptions (approaching 194 dB at close range).

Important: This limit applies to sound pressure level (SPL) in air. In other media (water, solids) or at different atmospheric pressures, the maximum would differ.

Formula	Usage
dB = 10 × log₁₀(P₁/P₀)	Power, intensity
dB = 20 × log₁₀(V₁/V₀)	Voltage, pressure, amplitude
L = 10 × log₁₀(Σ10^(Lᵢ/10))	Adding sound sources
L₂ = L₁ − 20 × log₁₀(d₂/d₁)	Distance attenuation