Compute the radiated sound power level L_W of a machine using the ISO 3744 free-field engineering method. Change the measurement surface, microphone count, averaged SPL, background noise and environmental K2 to see the K1 correction, corrected SPL, L_W, uncertainty and measurement grade update in real time.
Parameters
Measurement surface
Virtual surface enclosing the source
Microphone count N
Equal-area microphone positions on the surface
Measurement radius r
m
Averaged SPL ⟨L_p⟩
dB(A)
Energy average of N time-averaged SPLs
Background SPL L_bg
dB(A)
Ambient noise measured with the machine off
Environmental K₂
dB
Lift from reflections. ≤2 dB targets engineering grade
Meter accuracy
dB
Stand-alone sound-level-meter uncertainty. Class 1 ≈ 0.7 dB
Results
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Surface area S (m²)
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Background K₁ (dB)
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Corrected Lp (dB(A))
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Sound power L_W (dB(A))
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Uncertainty (dB)
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Measurement grade
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Measurement surface and microphone layout
A central machine is surrounded by N microphones (red dots) on the hemispherical surface; their averaged SPL plus the surface area gives L_W. The green dashed arc shows the measurement radius r.
Combined standard uncertainty: meter accuracy, half the environmental correction (standard uncertainty of K₂) and a method-intrinsic term, combined in quadrature.
Sound Power Level Measurement — ISO 3744 Free-Field Method
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Is "sound power level" a different thing from SPL? I saw an L_WA value on a washing-machine spec sheet and wasn't sure what it meant.
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Completely different quantities. SPL (L_p) is the loudness at a particular point and depends on distance and room reflections. Sound power level L_W is the energy the machine emits per second, expressed in dB, and it depends on neither distance nor room — it's an intrinsic property of the source. That's why catalogues use it: you can compare two machines fairly. A "53 dB(A)" on a washing-machine sheet is almost always L_WA (A-weighted sound power level), not the SPL you would measure standing in front of it.
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So how do you actually measure L_W? You can buy an SPL meter off the shelf, but you can't directly measure power, right?
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Exactly. Since you can't measure power directly, you measure SPL at many points on an imaginary surface around the machine and multiply by the surface area. The relation is L_W = ⟨L_p⟩ + 10·log₁₀(S/S₀), where S is the surface area (2πr² for a hemisphere). ISO 3744 is the global standard and guarantees engineering-grade accuracy of ±1.5 dB. Switch the "Measurement surface" on the left between hemisphere, parallelepiped and conformal — you'll see S change a lot, and L_W moves with it even at the same ⟨L_p⟩.
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What are K₁ and K₂? They look like corrections, and we subtract both?
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Both are corrections that take the measured value down from an overestimate. K₁ is the background correction — it removes the portion of ⟨L_p⟩ that is really the room background L_bg leaking through. The bigger the margin ΔLp = ⟨L_p⟩ − L_bg, the smaller the correction: 0 for ΔLp ≥ 15 dB, about 0.46 dB at 10 dB and 1.26 dB at 6 dB. Below 6 dB the background is too strong and ISO 3744 declares the test invalid. K₂ is the environmental correction for sound reflected back from the walls and floor — typically 1-2 dB in a semi-anechoic room and 3-5 dB in an ordinary factory.
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The microphone count is set to 10 by default. Is more always better?
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ISO 3744 requires at least 10 standard positions on the hemisphere and 9 on the parallelepiped — fewer than that isn't a valid test (the tool warns you). More positions stabilises the spatial average and lowers uncertainty, but the benefit largely saturates by 12-20 positions. For highly directional machines like a fan's intake mouth, you push it to 20+ or switch to the conformal method and sample densely on a surface at 1 m from the product outline.
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There's "engineering" and "survey" grade — when do you use each?
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Engineering grade (ISO 3744, ±1.5 dB) is for "numbers that go public" — catalogue ratings, regulatory compliance, type approval. It requires K₂ ≤ 2 dB and a Class 1 meter (accuracy ≤ 0.7 dB). Survey grade (ISO 3746, ±3 dB) is for in-plant spot checks, before/after comparisons and occupational-health screening — a rougher outdoor measurement or a Class 2 meter falls here. If you need even more accuracy, you step up to precision grade (ISO 3741, ±0.5 dB) using a reverberation room. Drag K₂ and the meter accuracy on the left and watch the grade flip in real time.
Frequently Asked Questions
ISO 3744 is the engineering-grade method (uncertainty ±1.5 dB) for sound power in a free field over a reflecting plane — typically a semi-anechoic room or flat outdoor site. ISO 3746 covers the same free field but at survey grade (±3 dB) with relaxed microphone counts and environmental requirements. ISO 3741 uses a reverberation room for precision grade (±0.5 dB) used in research and reference-source calibration. The dB(A) ratings on consumer-product datasheets are almost all ISO 3744 results.
K1 is set by the difference ΔL = L_p − L_bg between the operating SPL and the background SPL measured with the machine off. For ΔL ≥ 15 dB, K1 = 0 (background ignored). For 10 ≤ ΔL < 15 dB, K1 = −10·log10(1 − 10^(−ΔL/10)), giving less than 0.3 dB. For 6 ≤ ΔL < 10 dB the same formula yields up to 1.3 dB. Below 6 dB, the background dominates and ISO 3744 considers the test invalid; only a capped 1.3 dB correction is applied and the value is treated as indicative.
K2 accounts for the way reflections from walls and floor raise the SPL on the measurement surface. It depends on the room absorption and the machine-to-wall distance: typically 1-2 dB in a semi-anechoic room, 3-5 dB on a generic factory floor and 6-7 dB in a live room. To reduce it: (1) add absorptive material on walls and ceiling, (2) move the machine well away from walls (more than twice the measurement radius), or (3) move outdoors. K2 ≤ 2 dB is the engineering-grade target; K2 > 4 dB drops the test to survey grade.
ISO 3744 specifies a minimum of 10 standard microphone positions on the hemisphere and 9 on the parallelepiped. On the hemisphere they are distributed so each carries an equal area share around the source, and at each point the time-averaged SPL is measured. Adding microphones reduces uncertainty but the benefit saturates around 12-20 positions. Custom positions outside the standard set are not allowed by ISO 3744 — if a non-standard layout is needed, switch to the conformal method (a surface at a fixed distance from the product outline) with at least 20 points.
Real-World Applications
Consumer-appliance and office-equipment noise labels: Washing machines, outdoor AC units, refrigerators and laser printers — the L_WA ratings on the spec sheets for almost every household and office product are measured with ISO 3744. The EU Ecodesign directives and the Japanese energy-label scheme require sound-power declarations, so engineers set target dB(A) values up front and use tools like this to optimise the test surface and room conditions.
Industrial and construction machinery: Injection-moulding machines, compressors, hydraulic pumps and generators are shipped after ISO 3744 acceptance tests at an outdoor flat site or factory semi-anechoic room. The EU Outdoor Noise Directive 2000/14/EC requires L_WA declarations for outdoor equipment, often using large hemispheres of 4-10 m radius. Sweep the measurement radius in this tool and you see S grow as r², so L_W increases at the same SPL.
HVAC equipment, fans and ducts: Beyond ISO 3744, fans and air-handling units often use sector standards such as AMCA 300 (North America) or ISO 13347 (in-duct). For building-services design the equipment L_W is the input to room SPL prediction (NC-rating checks), making L_W the most important starting point of the entire acoustic calculation.
Automotive, toys and power tools: Vehicle pass-by noise has its own ISO 362 procedure, but engine bare-unit tests, accessory (alternator, water pump) and electric-motor development use ISO 3744 L_W as the basis for predicting in-vehicle noise. Toy regulations EN 71-1 and power-tool regulations EN 60745 both set sound-power limits in the same way.
Common Misconceptions and Pitfalls
The first pitfall is "L_W shouldn't depend on the measurement radius, so I can pick any radius". In theory L_W is intrinsic to the source, but in practice there is a sweet spot. Too small a radius (e.g. r < 1 m) puts microphones in the near field where the source no longer looks like a point and the surface SPL varies wildly, exploding the spatial-average uncertainty. Too large a radius makes ΔLp = ⟨L_p⟩ − L_bg shrink, the K₁ correction grows and below 6 dB the test is simply invalid. ISO 3744 recommends r ≥ 1 m and at least half the largest machine dimension, with 2-4 m being typical for production-equipment-sized sources.
The second misconception is "comparing L_W directly to a regulatory SPL limit". A "55 dB(A) environmental limit" is an SPL limit at the receiver, not on the source's L_W. A machine with L_W = 87 dB(A) gives, at 10 m in a free field, L_p = L_W − 10·log₁₀(2π·10²) ≈ 87 − 28 = 59 dB(A). Reading a catalogue L_WA as if it were the receiver SPL and panicking about a violation is one of the most common errors in the field. Converting L_W to L_p requires distance, directivity index DI, and (for diffuse-field interiors) the 10·log(4/R) room term — this simulator handles only the source-side L_W.
Third: "K₂ = 0 must be the most accurate setting". K₂ = 0 means a perfect free field (anechoic chamber or open sky); in any real semi-anechoic room or outdoor site you will always have at least about 1 dB. A test reporting K₂ = 0 without passing the ISO 3744 qualification procedure (where a reference source is measured to lie within ±0.5 dB) won't be trusted. The proper practice is not to push K₂ to zero but to use the K₂ value measured from your room's qualification test. Also remember that dB(A) is the A-weighted value matched to human hearing — it is not the same as the physical radiated power, and a low-frequency-heavy machine will be under-stated by dB(A) compared with its actual energy.
How to Use
Enter the number of measurement microphone positions (typically 6–12 points per ISO 3744)
Input the hemispherical or rectangular surface radius in meters (e.g., 1.0 m for a small pump, 2.0 m for industrial motors)
Record the spatially-averaged sound pressure level L_p in dB(A) from all microphone positions
Enter the background noise level at your test location in dB(A)
The simulator calculates surface area S, applies background correction K₁, computes corrected pressure level, and derives radiated sound power L_W in dB(A) with measurement uncertainty
Worked Example
For a 7.5 kW electric motor tested in a semi-anechoic chamber: 8 measurement points arranged on a hemisphere of radius 1.0 m yield surface area S = 6.28 m². Averaged L_p = 82.5 dB(A), background noise = 70 dB(A). Background correction K₁ = 2.1 dB (since 82.5 − 70 = 12.5 dB exceeds the 6 dB threshold). Corrected L_p = 80.4 dB(A). Sound power level L_W = 80.4 + 10·log₁₀(6.28) = 88.3 dB(A), with uncertainty ±1.5 dB for Grade 2 (engineering-grade) measurement.
Practical Notes
Use hemispherical surfaces (180° coverage) for machines mounted on reflecting floors; rectangular surfaces suit free-standing equipment in anechoic or semi-anechoic rooms per ISO 3744:2017
Ensure background noise is at least 6 dB below measured L_p; if closer, K₁ correction increases and uncertainty widens
Microphone spacing should be approximately equal; ISO 3744 specifies exact grid positions for 6, 8, or 10 points to minimize sampling error
For Grade 1 (precision) work on reference standards, uncertainty ±0.8 dB; Grade 2 (engineering) allows ±1.5–2.0 dB, suitable for compliance declarations