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Inverse square law for intensity calculator

A-level Waves

The intensity from a small source spreading evenly in all directions.

I = P / (4πr²)

This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

IIntensity to find 0.884 W/m² W/m²

PPower of the point source

rDistance from the source

Significant figures

Working

Write the equation
I = P / (4πr²)
Substitute the values
I = 100 ÷ (4π × 3²)
Calculate
I = 0.884194 W/m²
Give the answer to 3 significant figures
I = 0.884 W/m²

Worked example

Find I, the intensity. Given: power of the point source P = 100 W; distance from the source r = 3.00 m.

Write the equation
I = P / (4πr²)
Substitute the values
I = 100 ÷ (4π × 3²)
Calculate
I = 0.884194 W/m²
Give the answer to 3 significant figures
I = 0.884 W/m²

Symbols and units

Symbol	Quantity	SI unit
I	Intensity	W/m²
P	Power of the point source	W
r	Distance from the source	m

Inverse square law for intensity: rearranged

To find intensity: I = P / (4πr²)
To find power of the point source: P = 4πI r²
To find distance from the source: r = √(P / (4πI))

Exam tip

Doubling the distance makes the intensity four times smaller.

Common questions

What is the formula for inverse square law for intensity?

The equation is I = P / (4πr²), where I is the intensity (W/m²); P is the power of the point source (W); r is the distance from the source (m).

What units should I use for inverse square law for intensity?

In SI units: intensity in W/m², power of the point source in W, distance from the source in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange I = P / (4πr²)?

Rearranging gives these forms: to find intensity: I = P / (4πr²). to find power of the point source: P = 4πI r². to find distance from the source: r = √(P / (4πI)).

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Read the full explanation on the Inverse-square law for intensity formula page. More waves equations: Wave speed, Frequency and time period, Magnification, Refractive index, Snell’s law, Critical angle, Double-slit fringe spacing, Diffraction grating. See the full list on the a-level physics equation calculator page.