Beam Diameter Conversion
Convert Gaussian beam diameters between the 1/e², 1/e and FWHM definitions and the waist radius w₀, with relative intensity levels.
Educational only — not compliance-grade
These pages implement the published exposure limits for the cases each one states, but they are educational tools: no laser safety officer has signed them off.
- Do not use these results alone for PPE selection, NHZ / NOHD approval, controlled-area sign-off, enclosure/interlock approval, or formal classification.
- Always verify against ANSI Z136.1, IEC 60825-1, your local procedures, and the responsible laser safety officer / CLSO.
Conversion Formulas
d1/e = d1/e² / √2 ≈ 0.7071 d1/e²
dFWHM = d1/e² × √(ln 2 / 2) ≈ 0.5887 d1/e²
w = d1/e² / 2
I(r) = I₀ exp(−2r²/w²)
P(inside d) / P = 1 − exp(−d² / (2w²))
The IEC 60825-1 and ANSI Z136.1 “beam diameter”, used in the exposure limits and hazard distances, is the 1/e diameter (the circle that holds 63 % of the power). Datasheets often quote the 1/e² diameter instead, which is √2 larger.
Input
Results
1/e² diameter
1.0000 mm
86.47 % of the power inside
1/e diameter
0.70711 mm
63.21 % of the power inside
FWHM
0.58871 mm
50.00 % of the power inside
Beam radius w (1/e²)
0.50000 mm
w = d(1/e²) / 2
Intensity Ratios (relative to peak)
Gaussian Beam Profile
Model and references
Exact. The equations are exact within the stated assumptions, or are a standard's tabulated values. The results are as good as the inputs. About the tiers
TEM₀₀ round beam I = I₀ exp(−2r²/w²): d(1/e²) = 2w, d(1/e) = d(1/e²)/√2, FWHM = √(ln2/2) d(1/e²) = 0.5887 d(1/e²). Not modelled: elliptical or non-Gaussian beams, second-moment widths.
- Saleh B. E. A., Teich M. C. (1991). Fundamentals of Photonics, ch. 3 (Beam Optics): Gaussian beam intensity and power. Wiley. doi:10.1002/0471213748