Track intensity drop with distance using inverse square relations for checks daily. Pick compare or source modes, enter values, and export results now easily.
| Case | I1 | r1 | r2 | Expected I2 |
|---|---|---|---|---|
| Doubling distance | 200 W/m² | 2 m | 4 m | 50 W/m² |
| Tripling distance | 90 W/m² | 1 m | 3 m | 10 W/m² |
| Half distance | 15 W/m² | 6 m | 3 m | 60 W/m² |
The inverse square relationship states that intensity decreases with distance squared: I ∝ 1 / r².
Inverse-square behavior appears whenever a fixed amount of energy spreads uniformly over a growing area. For light, sound, radiation, and gravitational or electric influence, the effective area increases with distance squared, so the measured intensity falls rapidly as you move away.
Doubling distance reduces intensity to one quarter. Tripling distance reduces it to one ninth. This steep drop explains why sensors saturate near sources yet struggle at longer ranges. It also guides safe spacing for high-intensity emitters and accurate placement for detectors.
Field measurements often provide one reliable reference reading. Using I2 = I1 × (r1²/r2²), you can predict the intensity at a new location without re-measuring. If the prediction differs from observation, the source may not be point-like or the medium may absorb energy.
When intensity at a second point is known, rearranging gives r2 = r1 × √(I1/I2). This is useful in photometry, acoustic mapping, and quick range estimation where geometry is simple and the emission is steady.
For a true isotropic point source, power spreads over the surface of a sphere. That surface area is 4πr², so intensity becomes I = P/(4πr²). The calculator includes a simple r² option when your problem uses a proportional form or a reduced solid-angle setup.
A 100 W isotropic source produces about 0.80 W/m² at 10 m using 4πr². At 20 m it falls to about 0.20 W/m². These values highlight why measurement noise and detector sensitivity matter more as distance grows.
Real systems deviate due to reflections, beam shaping, shielding, absorption, or near-field effects. Directional sources concentrate energy into smaller solid angles, increasing intensity compared with isotropic spreading. In air or water, attenuation adds an exponential loss that stacks on top of inverse-square scaling.
Use comparison mode for quick checks between two stations, and point-source mode when power or strength is the known quantity. Document units carefully, keep distances positive, and treat large discrepancies as evidence to revisit geometry, alignment, or environmental losses.
In lighting design, inverse-square checks estimate lux across work zones. In astronomy, observed flux follows the same geometry, supporting distance comparisons with known intrinsic luminosity.
It describes how intensity from a point-like source decreases as distance increases. When distance doubles, intensity becomes one quarter, assuming uniform spreading and no absorption.
Use comparison mode when you have intensity readings at one distance and want another distance. Use point-source mode when source power or strength is known and you need intensity or distance.
A true isotropic source spreads power over a spherical surface area of 4πr². The 4π option converts power to intensity using that physical geometry.
Yes. Many radial influences scale with 1/r². The calculator helps with ratios and distance scaling, but units and constants depend on the specific law you are modeling.
Reflections, directionality, shielding, absorption, and near-field behavior can break simple spreading assumptions. Check alignment, medium losses, and whether the source is truly point-like.
Pick any consistent units. Distances must match each other, and intensity units must match between I1 and I2. Units are displayed as labels and do not change the math.
No. Solving distance uses a ratio or division by intensity. Enter a positive, nonzero intensity for the target point to avoid undefined results.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.