🔊 Sound Decibel Calculator

Convert between dB and intensity, and combine multiple sound sources.

Convert from

Intensity I (W/m²)

Sound Level (dB)

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Result

Decibel Reference Chart

How to Use This Calculator

This calculator has two modes. The first converts between intensity in W/m² and decibels. The second combines multiple sound sources to find the total level. Use the reference chart at the bottom to get a feel for where your result sits on the loudness scale.

Select the "dB to Intensity" or "Intensity to dB" direction depending on what you know.

For intensity input, enter the value in W/m². A quiet room might be around 10⁻¹⁰ W/m² (40 dB). Type scientific notation like 1e-10.

To combine sources, click the "Combine Sources" tab, add each source level in dB, and click Calculate Combined Level.

Check the reference chart to see how your result compares to everyday sounds.

Decibel Formula

L = 10 × log₁₀(I / I₀) [dB] I = I₀ × 10^(L / 10) [W/m²] I₀ = 1 × 10⁻¹² W/m² (threshold of hearing) Combined: L_total = 10 × log₁₀(10^(L₁/10) + 10^(L₂/10) + ...)

Every 10 dB increase represents a tenfold increase in intensity. But human perception is different: a 10 dB increase sounds about twice as loud. This is why whispered conversation at 30 dB feels very quiet compared to normal speech at 60 dB, even though the intensity ratio is 1000:1.

Worked Examples

Intensity 10⁻⁶ W/m² converted to dBL = 10 × log₁₀(10⁻⁶ / 10⁻¹²) = 60 dB

70 dB source converted to intensityI = 10⁻¹² × 10^7 = 10⁻⁵ W/m²

Two 70 dB sources combinedL_total = 73 dB (not 140 dB)

Four identical sources of 65 dB eachL_total = 71.02 dB

Where This Comes Up in Real Life

Workplace noise regulations use decibel limits to protect hearing. OSHA sets an 85 dB limit for 8 hours of continuous exposure per day. At 91 dB, the allowed exposure drops to 2 hours. Above 115 dB, any exposure without hearing protection is prohibited. Using the formula, 85 dB corresponds to an intensity of I = 10⁻¹² × 10^8.5 = 3.16 × 10⁻⁴ W/m², which sounds abstract until you know it is comparable to a lawnmower at close range.

Concert venue designers need to calculate the combined level from multiple speaker stacks. Adding a second stack of equal output does not double the decibels: it adds only 3 dB. To achieve a 10 dB boost (which sounds about twice as loud), you need 10 times the number of identical sources. This is why large arenas use dozens of delayed speaker arrays rather than just turning up one central cluster.

Frequently Asked Questions

What is a decibel?

A decibel (dB) is a logarithmic unit for sound intensity. dB = 10 × log₁₀(I / I₀), where I₀ = 10⁻¹² W/m² (threshold of hearing).

Why use a logarithmic scale?

Human hearing spans ~12 orders of magnitude in intensity (0 dB to 120 dB). The logarithmic scale compresses this into a manageable range and matches how we perceive loudness.

How much louder is 10 dB?

Every 10 dB increase represents a 10× increase in intensity. But perceptually, ~10 dB sounds about twice as loud.

What are safe decibel levels?

Below 70 dB: safe. 85 dB: 8 hours maximum (OSHA). 100 dB: 15 minutes. Above 120 dB: immediate ear damage.

Do two identical sounds add to double dB?

No. Two 70 dB sources together produce ~73 dB (3 dB increase), not 140 dB. Doubling intensity adds 3 dB.