How does distance affect speaker loudness (SPL)?

Based on the Inverse Square Law, sound pressure level (SPL) decreases by 6dB for every doubling of the distance from the source in an open environment.

How much amplifier power is needed for a 3dB gain?

You must double the amplifier wattage to achieve a 3dB increase in SPL. For a 10dB gain (roughly twice as loud), you need 10 times the power.

Sound Level(dB) with Sound Pressure Level Calculator

Estimate Sound & Pressure Level at a distance.

Speaker Sensitivity (dB at 1W/1m)

Amplifier Power (Watts)

Distance (Meters)

SPL at Distance -- dB

SPL at 1 Meter -- dB

What is Sound Pressure Level (SPL)?

Sound Pressure Level (SPL) is the objective measure of the "loudness" of a sound wave relative to the threshold of human hearing (20 µPa). Because the human ear has a massive dynamic range, we use the decibel (dB) log scale.

This calculator determines how loud a speaker will be at a specific distance, based on its manufacturer specifications (Sensitivity) and the amplifier power.

The Inverse Square Law

Sound spreads out as a sphere. As the radius of the sphere doubles, the energy is spread over 4x the area. This leads to the fundamental rule of acoustics:

Every doubling of distance = -6 dB drop in SPL

The Physics of Sound Loss

Sound doesn't stay at the same volume as it travels. In an "open field" (free space), sound spreads out in a sphere. The further you are from the source, the more the energy is spread out.

Total SPL = Sensitivity + 10 log₁₀(Power) - 20 log₁₀(Distance)

Inverse Square Law Diagram showing sound pressure drop over distance

Figure 1: Visual representation of the Inverse Square Law in audio.

[Image of the inverse square law for sound]

Practical Applications

Home Theater: Ensuring your amplifier has enough headroom to reach peak volumes at the listening position.
PA Design: Calculating the effective "throw" of a speaker in a large hall or outdoor venue.

Calculation Formula

SPL_dist = SPL_1m - 20×log₁₀(Distance)

Where SPL_1m is the SPL at 1 meter, calculated from the speaker's sensitivity and input power:

SPL_1m = Sensitivity + 10×log₁₀(Power)

Practical Applications

Concerts & Events: Audio engineers use this to calculate how many speakers and watts are needed so that people in the back row (50m away) can still hear clearly.
Safety (OSHA): Determining if machinery noise levels at a worker's station exceed safe limits (85 dB).
Home Theater: Calibrating speakers to "Reference Level" (usually 85 dB or 75 dB) at the listening position.

FAQ

Does doubling power double loudness?

No. Doubling the power (e.g., 100W to 200W) only adds +3 dB. To double the perceived loudness (which requires roughly +10 dB), you need 10x the power!

What is "A-Weighting"?

dBA or A-weighting is a filter that alters the reading to match human hearing. Our ears are less sensitive to bass and treble. This calculator assumes flat (Z-weighted) response, but dBA is used for safety/legal noise limits.

What is the "Threshold of Pain"?

Around 120-130 dB SPL. At this level, sound becomes physical pain and instant hearing damage can occur. A jet engine taking off is ~140 dB.