dB Addition Calculator (Two Sound Sources)

Enter the decibel levels of two sound sources to calculate their logarithmically combined level, increase over the louder source, and each source's energy contribution.

Created by Luis GonzalezLast updated: May 9, 2026

How to Use This Calculator

1
Enter Source 1 Level
Input the sound pressure level of your first sound source in decibels (dB SPL).
2
Enter Source 2 Level
Input the sound pressure level of your second sound source in decibels (dB SPL).
3
Review Combined Sound Level
Examine the total combined sound level, the increase over the loudest source, and the energy share of each source.

Example Calculation

An audio engineer wants to know the combined sound level of two identical sound sources, each producing 80 dB.

Source 1 Level (dB)

Source 2 Level (dB)

Results

83.01 dB

Tips

Understand the 3 dB Rule

When two identical, uncorrelated sound sources are combined, the total sound pressure level increases by approximately 3 dB, not 6 dB. This logarithmic behavior is fundamental to decibel calculations.

Consider Phase Coherence

This calculator assumes uncorrelated sources. If sources are perfectly coherent and in phase (e.g., two identical loudspeakers fed the same signal in a very specific setup), the theoretical increase can be up to 6 dB, but this is rare in real-world scenarios.

Account for Distance and Environment

The combined level is highly dependent on the listener's position relative to each source and the acoustic properties of the room. Sound levels decrease with distance (inverse square law) and are affected by reflections and absorption.

The dB Addition Calculator helps audio engineers, environmental scientists, and safety officers accurately combine the sound levels of two distinct sources. Since decibels are a logarithmic unit, they do not add arithmetically. This tool performs the correct logarithmic sum, revealing the true combined sound pressure level and each source's energy share. For example, two identical 80 dB sources do not combine to 160 dB; instead, they sum to approximately 83.01 dB, demonstrating the non-linear nature of sound perception and measurement critical for noise assessments in 2025.

Understanding the Logarithmic Nature of Sound Addition

When dealing with sound, intuition can often be misleading. Two sound sources, each producing 80 dB, don't combine to make 160 dB. This is because decibels measure a ratio of sound power on a logarithmic scale, mimicking how human ears perceive loudness. The actual acoustic energy (power) from the sources adds arithmetically, but that sum is then converted back to the logarithmic decibel scale. This means that combining two equal sound sources typically results in a +3 dB increase, a key principle in acoustics and noise control.

The formula for adding two sound pressure levels (L1 and L2) in decibels is:

total dB = 10 × log10(10^(L1/10) + 10^(L2/10))

Where:

L1 is the decibel level of Source 1
L2 is the decibel level of Source 2
log10 is the base-10 logarithm

💡 For musicians and content creators, understanding combined sound levels is crucial when mixing. Our Streaming Loudness Target Calculator helps you meet platform-specific loudness standards.

Combining Two Identical Sound Sources

Let's consider a scenario where an engineer needs to determine the combined sound level from two identical machines operating simultaneously.

Source 1 Level: The first machine produces a sound level of 80 dB.
Source 2 Level: The second machine also produces a sound level of 80 dB.
Convert to Linear Power Ratio:
- For Source 1: 10^(80/10) = 10^8
- For Source 2: 10^(80/10) = 10^8
Sum Linear Power Ratios: 10^8 + 10^8 = 2 × 10^8
Convert Back to Decibels: 10 × log10(2 × 10^8) = 10 × (log10(2) + log10(10^8)) = 10 × (0.30103 + 8) = 10 × 8.30103 ≈ 83.01 dB.

The Combined Level from these two 80 dB sources is 83.01 dB, an increase of approximately 3.01 dB over the loudest (and only) individual source. This confirms the logarithmic nature of decibel addition.

💡 For more advanced audio system design, especially concerning low-frequency reproduction, our Subwoofer Box Volume Calculator (Sealed) can help optimize enclosure dimensions.

Practical Applications of Sound Pressure Levels

Understanding sound pressure levels (SPL) is crucial across various domains. In environmental noise assessments, SPL helps characterize noise pollution from traffic (e.g., busy street 70 dB), industrial sites, or aircraft. In occupational health, regulatory bodies like OSHA set permissible exposure limits, such as 85 dBA for an 8-hour workday, emphasizing that prolonged exposure above this can cause hearing damage. Acoustic engineers use SPL to design concert halls (often aiming for 100-110 dB peaks) or recording studios, where background noise should be minimized (e.g., quiet office 40 dB). The concept of a 3 dB increase representing a doubling of sound energy is fundamental, as is the inverse square law, which states that sound intensity decreases by 6 dB for every doubling of distance from the source in a free field.

The Origins and Importance of the Decibel Scale

The decibel (dB) scale, developed by Bell Telephone Laboratories in the 1920s, originated from the need to quantify signal loss over long telephone lines. It was named after Alexander Graham Bell and is a logarithmic unit used to express the ratio of two values of a physical quantity, often power or intensity. The logarithmic nature of the decibel scale is particularly well-suited to human perception, as our senses (hearing, sight) respond logarithmically to stimuli rather than linearly. This allows a vast range of sound intensities, from the rustle of leaves (around 20 dB) to a jet engine (around 140 dB), to be represented by a manageable numerical scale, making it indispensable in acoustics, electronics, and telecommunications for comparing signal strengths and noise levels.

Frequently Asked Questions

Why don't decibels add linearly like regular numbers?

Decibels are a logarithmic unit, meaning they represent a ratio of power or intensity rather than an absolute value. Because human hearing perceives sound on a logarithmic scale, decibels are used to compress a vast range of sound pressures into a more manageable numerical scale. Therefore, combining two sound sources involves adding their power ratios logarithmically, not their decibel values linearly.

What does it mean for sound energy to 'double'?

For sound, a doubling of acoustic energy (or power) corresponds to an increase of approximately 3 dB. This is a crucial concept in audio; for example, if you add a second identical speaker, the overall sound power doubles, but the perceived loudness only increases slightly, by 3 dB. A perceived doubling of *loudness* typically requires a 10 dB increase.

What is the difference between dB SPL and other dB measurements?

dB SPL (Sound Pressure Level) measures the absolute sound pressure relative to a reference (usually 20 micropascals, the threshold of human hearing) and is used for environmental noise or acoustic measurements. Other dB measurements, like dBm (relative to 1 milliwatt) or dBu (relative to 0.775 volts), refer to electrical power or voltage levels in audio equipment, not acoustic pressure.

When is it important to add decibels accurately?

Accurately adding decibels is critical in various fields, including environmental noise assessment (e.g., combining traffic noise and industrial noise), acoustic design of concert halls or recording studios, and occupational health and safety to ensure worker exposure remains below hazardous thresholds. It ensures proper system design and regulatory compliance.