Hair Diffraction Calculator — Measure Hair Diameter with a Laser
A classic physics experiment: shine a laser through (or past) a single hair and measure the dark-band positions on a distant screen. Because the hair acts as a single-slit diffracting obstacle (Babinet's principle), the fringe spacing reveals the hair diameter. Enter the laser wavelength, the screen distance and the dark-fringe position to compute the hair diameter in micrometres.
nm
cm
(integer)
mm
Within the typical human hair range (50–150 μm) — consistent with a human hair.
- 1
sin θ = y ÷ √(L² + y²)
5 ÷ √(1,000² + 5²) = 0.005Screen distance and fringe position both in mm; ratio is dimensionless. - 2
Diameter in nm
1 × 633 nm ÷ 0.005 = 126,601.6 nm - 3
Diameter in μm
126,601.6 nm ÷ 1 000 = 126.6 μm
How does this calculator work?
Shine a laser past a hair and measure the dark fringe at distance y from centre on a screen at distance L. The hair diameter is d = m × λ / sin(arctan(y/L)) ≈ m × λ × L / y for small angles. Enter the wavelength (nm), L (cm), fringe order m (integer) and y (mm) to get the diameter in μm. Typical human hair: 50–150 μm.
Formula
How this is calculated
Single-slit diffraction occurs when light passes through (or is blocked by) an obstacle of width d comparable to its wavelength. The diffraction condition for destructive interference (dark fringes) is d × sin θ = m × λ, where m is a positive integer (the fringe order) and λ is the wavelength. For small angles, sin θ ≈ tan θ = y/L where y is the fringe distance from the central maximum and L is the distance to the screen, giving d = m × λ × L / y.
By Babinet's principle, an opaque obstacle (such as a hair) produces the same diffraction pattern as a transparent slit of the same width, so you can measure the hair diameter directly from the fringe pattern rather than having to create a slit of the same size. The first dark fringe (m = 1) is typically the easiest to locate; using higher-order fringes (m = 2, 3, …) and averaging the inferred diameters gives a more accurate result.
This calculator uses the exact formula d = m × λ / sin θ (where sin θ = y / √(y² + L²)), which is slightly more accurate than the small-angle approximation when the fringe position y is not negligible compared to L. Human scalp hair typically ranges from 50 to 150 μm in diameter, with 70–90 μm being most common; the result flags whether it falls within this range. Typical lab uncertainties of 1–2 mm in fringe position translate to a few percent uncertainty in the inferred diameter.
Frequently asked questions
Any laser pointer works. Red (633–650 nm) and green (532 nm) pointers are the most common. A brighter pointer makes the fringes easier to see in ambient light. The wavelength is printed on most laser pointers or their packaging; if not, use 650 nm for a red pointer and 532 nm for a green one.
Stretch a single hair taut across a card with a small slit or gap, or tape it across an index card with a hole. Shine the laser beam through the gap so it hits the hair. Project the diffraction pattern onto a wall or screen at least 50 cm away. Measure the distance L from hair to screen, then measure y from the central bright dot to the first (or m-th) dark band on either side.
At 100 cm screen distance and 5 mm fringe position, sin θ ≈ 0.04999 and the small-angle approximation gives d ≈ m λ L / y; the exact formula gives d = m λ / sin θ — a difference of only 0.1%. The approximation breaks down when y approaches L, so this calculator uses the exact formula for accuracy at all screen distances.
Also known as
TG we-Calculate Editorial Team. (2026). Hair Diffraction Calculator — Measure Hair Diameter with a Laser [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hair-diffraction-calculator
TG we-Calculate Editorial Team. "Hair Diffraction Calculator — Measure Hair Diameter with a Laser." TG we-Calculate. 2026. https://we-calculate.com/calculator/hair-diffraction-calculator.
TG we-Calculate Editorial Team, "Hair Diffraction Calculator — Measure Hair Diameter with a Laser," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hair-diffraction-calculator
@misc{wecalculate_hair_diffraction_calculator, title = {Hair Diffraction Calculator — Measure Hair Diameter with a Laser}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hair-diffraction-calculator}}, year = {2026}, note = {TG we-Calculate} }
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