Enter the maximum permissible exposure (MPE), beam diameter at the aperture, beam divergence, and laser power into the calculator to determine the nominal optical hazard distance.

Nominal Optical Hazard Distance Calculator

Enter any 4 values to calculate the missing variable

Nominal Optical Hazard Distance Formula

The following simplified relationship is often used to estimate the nominal optical hazard distance (NOHD) for a circular beam when you know the beam diameter at the aperture, the (full-angle) beam divergence, the laser power, and the applicable MPE (irradiance). For standards-based laser safety calculations, refer to ANSI Z136 and the appropriate wavelength/exposure-duration MPE tables.

\mathrm{NOHD}=\frac{1}{\theta}\sqrt{\frac{4P}{\pi\,\mathrm{MPE}}-d_0^2}

Variables:

  • NOHD is the nominal optical hazard distance
  • MPE is the maximum permissible exposure (irradiance, W/m²)
  • d0 is the beam diameter at the aperture (m)
  • θ is the beam divergence (full-angle, radians)
  • P is the laser power (W)

To estimate the NOHD, set the beam irradiance equal to the MPE at distance R, use the beam expansion model d(R) = √(d0² + (θR)²), then solve for R.

What is Nominal Optical Hazard Distance?

The nominal optical hazard distance (NOHD) is the distance from a laser source within which the beam irradiance (for continuous-wave lasers) or radiant exposure (for pulsed lasers) exceeds the applicable maximum permissible exposure (MPE) for the assumed exposure conditions. Beyond this distance, intrabeam viewing for those same assumptions is below the MPE. NOHD is a critical laser safety parameter used to define controlled areas and appropriate protective measures in medical, industrial, and research environments.

How to Calculate Nominal Optical Hazard Distance?

The following steps outline how to calculate the Nominal Optical Hazard Distance using the simplified model above.

  1. Determine the applicable maximum permissible exposure (MPE) as an irradiance in W/m² for your wavelength and exposure duration (per the relevant laser safety standard).
  2. Measure (or obtain from the laser specification) the beam diameter at the aperture, d0, in meters.
  3. Measure (or obtain) the beam divergence θ (full-angle) in radians.
  4. Measure the laser power (P) in watts.
  5. Calculate NOHD using NOHD = (1/θ) × √((4P)/(π·MPE) − d0²).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge (simplified model):

Maximum Permissible Exposure (MPE) = 10 W/m²

Beam Diameter at Aperture (d0) = 0.05 m

Beam Divergence (θ) = 20 mrad

Laser Power (P) = 2 W

NOHD = (1/0.02) × √((4×2)/(π×10) − 0.05²) ≈ 25.11 m