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Inverse-Square Spherical Sound Divergence (SPL) Calculator

In free and hemispherical acoustic fields, acoustic sound pressure drops by exactly 6 dB for each doubling of distance from a point source.

Calculated Result
72.0 dB SPL

Sound Pressure Level (Lp)

Geometric Attenuation

-28.0 dB

Directivity Space

Hemispherical Hard Ground (Q=2)

Calculation Breakdown

  1. Apply point source spherical dispersion equation Lp = Lw + 10·log10[Q / (4π·r²)]Lp = 100 + 10 * log10(2 / (4π * 10²)) = 72.0 dB

Sound Pressure Level vs Distance

Interactive visualization based on your current inputs

dB SPL
0.0234669921 m2 m5 m10 m20 mDistance (m)Lp (dB SPL)

What Is the Inverse-Square Spherical Sound Divergence (SPL) Calculator?

In free and hemispherical acoustic fields, acoustic sound pressure drops by exactly 6 dB for each doubling of distance from a point source.

How Does the Inverse-Square Spherical Sound Divergence (SPL) Calculator Work?

The calculation evaluates user-provided measurements using recognized domain equations, converts between measurement units, and adjusts for real-world efficiency factors.

Inverse-Square Spherical Sound Divergence (SPL) Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

L_p = L_w + 10 \log_{10}\left(\frac{Q}{4\pi r^2}\right) = L_w + 10\log_{10}(Q) - 20 \log_{10}(r) - 11

Geometric spreading disperses acoustic sound power over an expanding spherical or hemispherical wavefront surface area.

How to Use the Inverse-Square Spherical Sound Divergence (SPL) Calculator

  1. Enter your primary measurements in the input fields above.
  2. Select your preferred units (e.g. metric or imperial) if applicable.
  3. Review or adjust operational assumptions such as field efficiency.
  4. Click Calculate to instantly generate the full results breakdown and visual chart.
  5. Use the Reset button at any time to clear the form and test a new scenario.

Step-by-Step Example Calculation

100 dB Machine on Hard Ground at 10m

Input Values:

sourceSoundPowerLevelDb:100
distanceMeters:10
directivityFactorQ:2

Understanding Your Result

Your calculated result represents the realistic operational capacity or baseline output under the specified conditions. Comparing theoretical and effective outputs reveals the direct impact of turns, overlap, and practical downtime.

Factors That Affect the Result

Field terrain, operator experience, equipment maintenance, overlap margin, and weather conditions can significantly influence real-world output.

When Should You Use This Calculator?

Use this calculator whenever you need quick, verified estimates for job planning, budgeting, equipment sizing, or project timelines.

Assumptions & Limitations

  • Excludes atmospheric air absorption and ground excess attenuation.

Frequently Asked Questions

Calculation Accuracy & Reference Note

This calculator implements verified, deterministic mathematical equations based on published standards. Results should be treated as professional engineering estimates; always verify critical operations with local equipment manuals and site inspections.

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