Can any values expressed in dB be added together?

No. Inputs must represent the same physical level quantity, reference, frequency weighting or band, time basis and operating condition. Sound-pressure, sound-power, exposure, maximum and equivalent-continuous levels are not interchangeable merely because all use decibels.

When is 10 log10 summation valid for sound-pressure levels?

It is valid for compatible mean-square pressure contributions at the same receiver and time basis when the sources are mutually incoherent or uncorrelated and shared background is not counted repeatedly.

How are coherent tones combined?

Same-frequency pressure amplitudes with stable relative phases are combined as complex vectors. Two equal in-phase tones add about 6.0206 dB, while two ideal equal tones 180 degrees apart cancel in the mathematical model.

Can combined sound-power level predict receiver sound-pressure level?

No. Combined sound-power level describes total source emission under the stated independence assumptions. Receiver sound-pressure level additionally depends on directivity, distance, environment and propagation.

Does this worksheet determine occupational compliance?

No. It performs level-domain summation only. Exposure metrics require durations and the applicable framework, and no universal 85 dBA decision line is applied here.

Level-domain engineering worksheet

Acoustic Level Summation

Choose the physical model before adding decibels: incoherent pressure contributions, independent source sound powers, or coherent same-frequency pressure vectors.

same descriptorsame referencestable log-sumoptional phase model

Compatibility gate: “dB” is only a level unit. Do not mix sound pressure with sound power, dB with dBA, different frequency bands, different time weightings/averaging intervals, different receiver positions, sequential operating states, or measurements that each contain the same background.

Documented components

All fields start blank. Use each physical component once; do not count shared background repeatedly.

Summation model The selected model changes both the inputs and the equation.

Exact level descriptor Record quantity, reference, weighting/band and time basis—not merely “dB”.

Measurement/source and background record Identify how each component was obtained and how shared background or source interaction was excluded.

Select a model to display its physical prerequisites.

Sastāvdaļas

Component 1

Source/component

Līmenis (dB)

Component 2

Source/component

Līmenis (dB)

Component 3

Source/component

Līmenis (dB)

Component 4

Source/component

Līmenis (dB)

Component 5

Source/component

Līmenis (dB)

Component 6

Source/component

Līmenis (dB)

Component 7

Source/component

Līmenis (dB)

Component 8

Source/component

Līmenis (dB)

I checked compatibility: all components use the exact recorded descriptor and reference; pressure components refer to the same receiver and simultaneous time basis; shared background is removed or negligible; no source is already contained in another input; and the selected incoherence, independent-power or coherent-tone assumptions are supported.

Model 1 — mutually incoherent pressure contributions

For compatible mean-square sound-pressure levels from mutually incoherent simultaneous components at one receiver, the cross terms average to zero:

L_Σ = 10 log₁₀[Σ 10^Lᵢ/10]

Every Lᵢ must be the same descriptor: for example, all L_Aeq,15min at one receiver over the same interval, or all levels in the same one-third-octave band. Two equal incoherent components add exactly 10 log₁₀(2) = 3.0103 dB.

Model 2 — independent source sound powers

Independent acoustic powers add linearly, so compatible sound-power levels use the same 10 log₁₀ expression:

L_W,Σ = 10 log₁₀[Σ 10^L_W,i/10]

The output remains a sound-power level. It is not a receiver sound-pressure level and does not include directivity, distance, propagation, reflections or source interaction. If operating sources change one another’s emission, separately measured powers are not an independent-source model.

Model 3 — coherent same-frequency pressure components

For stable coherent tones at the same frequency and receiver, convert each pressure level to a relative amplitude and add complex pressure vectors:

p_Σ/p₀ = Σ 10^L_p,i/20 e^jφᵢ
L_p,Σ = 20 log₁₀|p_Σ/p₀|

Two equal in-phase components add 6.0206 dB; equal quadrature components add 3.0103 dB; ideal equal components 180° apart cancel. Real acoustic phase varies with frequency and position, so this mode is not valid for broadband levels, unstable phase, partial coherence or spatial averaging.

Compatibility and exclusion table

Question	Required answer	If not established
Same physical quantity and reference?	Yes: Lp with Lp, or Lw with Lw	Do not sum
Same weighting/band and time descriptor?	Jā	Reprocess the underlying data first
Same receiver and simultaneous pressure basis?	Yes for pressure modes	Do not present the result as a receiver total
Shared background counted once?	Removed, negligible, or explicitly isolated	Inputs can double-count energy
Correlation/coherence known?	Supported by the selected model	Cross-spectral information is required
Occupational exposure decision intended?	No—this is level summation only	Use a duration-based framework-specific exposure assessment

Sources and standards boundary

Equation classification: general logarithmic level relations derived from linear energy/power addition or coherent pressure superposition. They are not labelled as an ISO compliance calculation.

OSHA Technical Manual, Section III, Chapter 5, Appendix B.3 — official 10 log₁₀ summation of compatible pressure, intensity or power levels.
NIOSH Industrial Noise Control Manual — random-noise assumption and simultaneous-source energy addition.
NIST Special Publication 811 — 20 log₁₀ field-quantity and 10 log₁₀ power-quantity level definitions and the requirement to state the reference.
Boston University, The Decibel Scale — public instructional derivation distinguishing coherent amplitude addition from incoherent intensity addition.
ISO 80000-8:2020, Edition 2 + Amendment 1:2025 — current names, symbols, definitions and units for acoustical quantities.
IEC 61672-1:2013, Edition 2 — distinguishes frequency-weighted, time-weighted, time-averaged and exposure sound-level measurements.

Official records checked 13 July 2026. Partial-coherence cross terms, background-correction procedures and closed standard clauses are not guessed here.

Questions that prevent common errors

Can I mix dB and dBA?

No. “dB” alone does not identify the measured quantity or weighting. All inputs must have the same explicitly recorded descriptor.

Can I add measurements made with each machine on while the same background remains?

Not directly. Each reading then contains the background, so adding them counts that energy repeatedly. Use source-only contributions obtained through a justified isolation/background method, or measure the simultaneous total.

Can I add sequential tasks to obtain daily exposure?

Not with this simultaneous-source worksheet. Sequential exposure periods require duration-weighted energy integration or the formula specified by the governing exposure framework.

Why can a coherent result be below every component?

Coherent pressures can interfere destructively. The result depends on relative phase at the specific receiver and frequency; it is not an energy sum.

Is there an 85 dBA hearing-protection line?

No. A source-level sum is not automatically an eight-hour occupational exposure. OSHA, NIOSH and EU action/limit quantities differ and require duration and framework-specific assessment.