Laser Beam Expander Calculator

Our laser beam expander calculator will teach you everything you need to know about these simple devices.

Expander magnification10×f₂ ÷ f₁

Half-angle divergence0.000403 rad0.403 mrad, 1.3853 arcminutes

Full-angle divergence0.806 mraddatasheets quote either, so check which — they differ by a factor of two

Rayleigh range z_R1.2408 mthe distance over which the beam stays roughly collimated — the radius grows by √2 across it

Beam radius at 100 m40.3011 mm40.301 mm, 80.602× the waist

Beam diameter there80.6023 mm

Waist radius500 µm

Peak intensity at the waist1.273e+4 W/m²2P ÷ πw₀² — the on-axis peak of a Gaussian is twice the average over the spot

Peak intensity at 100 m1.96 W/m²0.0154% of the waist value

Against direct sunlight12.73×sunlight is about 1000 W/m² — a 5 mW laser beam concentrates far more than the Sun, which is why even low powers are an eye hazard

Expanded waist radius5 mm

Expanded divergence0.0403 mradreduced by exactly the magnification — expanding a beam is the only way to make it more collimated, because the product of waist and divergence is fixed by the wavelength

Expanded radius at 100 m6.4218 mmsmaller than the unexpanded beam at this range, despite starting larger

Waist × divergence2.015e-7 m·radequals λ/π for an ideal Gaussian beam — a conserved quantity, so you cannot have both a small waist and low divergence

The formula

θ = λ ÷ πw₀; w(z) = w₀√(1 + (z/z_R)²); z_R = πw₀² ÷ λ

Waist and divergence trade against each other

For an ideal Gaussian beam the product of waist radius and divergence half-angle is fixed at λ/π. That is a conservation law, not a limitation of engineering: a tightly focused beam necessarily spreads quickly, and a well-collimated beam must be wide. You cannot have both.

This is why beam expanders exist. Enlarging the beam by a factor of ten reduces its divergence by exactly ten, so although it starts wider it is narrower than the original at any useful range. Every long-range laser system — rangefinding, lidar, free-space optical links — expands the beam for this reason.

The Rayleigh range is the natural unit of distance. Within it the beam is roughly collimated; well beyond it the spread is essentially linear at the divergence angle. A 0.5 mm waist at 633 nm gives a Rayleigh range of about 1.2 m, so a laser pointer is already in its far field across a room.

On safety: a 5 mW beam concentrated into a half-millimetre waist reaches an intensity thousands of times that of direct sunlight. The eye focuses that to a far smaller spot on the retina, which is why milliwatt lasers are genuinely hazardous and why the blink reflex is not adequate protection.