Hair Diffraction Calculator (measure hair thickness with a laser pointer)

Understanding the hair diffraction calculator — concept and principle

This calculator measures the thickness of a hair from the diffraction pattern it makes when a laser pointer shines on it. You measure the dark spots on a screen, and it returns the hair diameter in micrometres. It is a classic home and classroom experiment in wave optics.

Thinner hair spreads the light wider; d = λ ÷ sin θ turns the 45 mm central band into a 57.8 µm hair.

How it is calculated

Dark spots: d sin θ = m λ, with tan θ = y ÷ L

d = m λ ÷ sin θ; small-angle estimate d ≈ m λ L ÷ y

λ is the laser wavelength (nm), L the hair-to-screen distance (m), y the distance from the centre to the m-th dark spot.
If you measure the width of the central bright band, y is half of it and m = 1.
Side fringes are spaced λL ÷ d apart.

The principle

Babinet's principle says a thin obstacle diffracts light in the same pattern as a slit of the same width, apart from the bright centre. For a slit, light from different parts of the opening cancels in certain directions, giving dark spots where d sin θ = mλ. Thinner hairs spread the pattern wider, so measuring the spread reveals the thickness, even though the hair is far too thin to measure with a ruler.

Worked example

Default inputs: 650 nm, screen 2 m away, central band width 45 mm, m = 1.

y = 45 ÷ 2 = 22.5 mm = 0.0225 m.
θ = atan(0.0225 ÷ 2) = 0.645°.
d = 650 × 10⁻⁹ ÷ sin(0.645°) = 57.8 µm; the small-angle estimate is also 57.8 µm.
Central band = 45 mm; side fringes are 650 × 10⁻⁹ × 2 ÷ 57.8 × 10⁻⁶ = 22.5 mm apart.

Each point is the calculator re-run with only “Measured distance (mm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Measured distance (mm)	Hair thickness (µm)
11.2	231.1
22.5	115.6
33.8	77
45	57.8
56.2	46.2
67.5	38.5
90	28.9

How to read the result

Human hairs are usually several tens of micrometres thick, so a result of a few tens to about 100 µm is plausible. A larger screen distance spreads the pattern and improves precision. Measuring across several dark spots and dividing reduces reading error.

Common mistakes

Using the full band width as y instead of half of it.
Entering the wavelength in micrometres instead of nanometres.
Measuring from the edge of the bright spot instead of the centre of the dark spot.
Using the wrong wavelength; red pointers vary from about 630 to 670 nm.

Keep in mind: Never look into the laser beam or its reflection, and do not point it at people or animals. Use a low-power pointer.

Frequently asked questions

Why does a hair act like a slit?

By Babinet's principle, complementary obstacles produce the same diffraction pattern away from the central spot.

What laser works best?

Any low-power pointer of known wavelength; green and red both work.

Does hair colour matter?

No. The positions of the dark spots depend on the hair's width, not on its colour.

Sources: OpenStax, University Physics Volume 3 (2016), section 4.1 "Single-Slit Diffraction"

Checked 9 Nov 2026. Single-slit minima a sin θ = mλ: OpenStax, University Physics Volume 3 (2016), Chapter 4 Key Equations (§4.1 “Single-Slit Diffraction”); Babinet’s principle for a thin obstacle (standard result).

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