M Square Calculator

The M² factor is a standard metric in optics and photonics used to describe the beam quality of a laser. Our calculator provides a conservative approach to design so that the final product integration can account for all possibilities of beam quality.

First, calculate the Beam Parameter Product (BPP).

BPP=FullAngleDivergence∗RodDiameterBPP=Full Angle Divergence*Rod Diameter

If unsure how to calculate the Full Angle Divergence, see the MegaWatt Lasers Beam Divergence Calculator. Note this calculator gives the Half Angle Divergence.

Once the BPP is calculated, the M² factor is:

M2=(π∗BPP)/λM^2=(π*BPP)/λ

M² Beam Quality Calculator

Calculate M² from full-angle divergence, rod diameter (used as beam waist diameter), and wavelength.

Beam Quality Factor

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M² ≥ 1 for real laser beams

Beam Radius w₀: —

Half-Angle Divergence θ: —

Beam Parameter Product: —

Rayleigh Range zR: —

Note: This calculator assumes that the entered rod diameter represents the beam diameter at the waist (w₀).
M² Calculation
M² = π w₀ θ / λ

w₀ = Rod Diameter ÷ 2

θ = Full-Angle Divergence ÷ 2

λ = Wavelength

  1. Koechner W. Solid-State Laser Engineering. 6th ed. New York, NY: Springer; 2006
  2. Paschotta R. M² Factor. RP Photonics Encyclopedia. RP Photonics AG. Available at: https://www.rp-photonics.com/m2_factor.html [Accessed August 2026]