Select a beam-model calculation and enter the required values in selected units. This educational estimate uses a supplied MPE; it does not calculate an exposure limit or establish laser safety.

Educational uniform-beam estimate. It does not determine MPE, protective eyewear, or a safe operating distance. A qualified laser safety assessment is required.

Use the applicable wavelength and exposure-duration limit supplied by a qualified laser safety assessment.

Small-angle model. Double a half-angle specification.

Nominal Optical Hazard Distance Formula

The calculator uses a simplified circular-beam irradiance model. It assumes a uniform beam profile and full-angle beam divergence. All calculations are performed in base units: meters, watts per square meter, watts, and radians.

d(R) = √(d₀² + (θ R)²)
MPE = (4P) / (π(d₀² + (θ R)²))
NOHD = R = (√((4P) / (π × MPE) - d₀²)) / (θ)

Rearranged formulas used when a different value is missing:

d₀ = √((4P) / (π × MPE) - (θ R)²)
P = (MPE × π) / (4)(d₀² + (θ R)²)
θ = (√((4P) / (π × MPE) - d₀²)) / (R)
  • NOHD or R: nominal optical hazard distance, the distance where the beam irradiance falls to the MPE.
  • MPE: maximum permissible exposure, entered as irradiance.
  • P: laser power.
  • d0: beam diameter at the aperture.
  • θ: full-angle beam divergence.
  • d(R): beam diameter at distance R.

Select the quantity to solve for. The irradiance mode calculates average beam irradiance at the entered distance, not a permissible-exposure limit. Supply the applicable MPE from a qualified laser safety assessment for the other modes.

Supported Units and Base Conversions

The calculator converts your entries to base units before applying the formulas, then converts the result back to the selected output unit.

Quantity Supported units Base unit used in formula
Distance and beam diameter m, ft, in m
MPE irradiance W/m², W/cm² W/m²
Laser power W, kW, HP W
Beam divergence mrad, rad rad

How Inputs Affect NOHD

Input change Effect on NOHD Reason
Higher laser power Increases NOHD More power requires more distance before irradiance falls to the MPE.
Higher MPE Decreases NOHD A higher exposure limit is reached closer to the source.
Larger divergence Decreases NOHD The beam spreads faster, reducing irradiance with distance.
Larger aperture beam diameter Usually decreases NOHD The same power is distributed over a larger starting area.

Example Calculations

Example 1: Calculate NOHD

Suppose you enter:

  • Laser power: 5 W
  • MPE: 25 W/m²
  • Beam diameter at aperture: 0.005 m
  • Beam divergence: 1 mrad, or 0.001 rad
NOHD = (√((4(5)) / (π(25)) - 0.005²)) / (0.001)
NOHD ≈ 504.6 m

The beam reaches the selected MPE at about 504.6 meters.

Example 2: Calculate laser power

Suppose you enter:

  • NOHD: 100 m
  • MPE: 25 W/m²
  • Beam diameter at aperture: 0.005 m
  • Beam divergence: 1 mrad, or 0.001 rad
P = (25π) / (4)(0.005² + (0.001 × 100)²)
P ≈ 0.1968 W

A laser power of about 0.197 W gives a 100 m NOHD under these assumptions.

FAQ

What does nominal optical hazard distance mean?

Nominal optical hazard distance is the distance from the laser aperture where the beam irradiance falls to the maximum permissible exposure. Inside that distance, direct exposure may exceed the selected MPE. Beyond that distance, this uniform-beam model predicts average irradiance at or below the supplied MPE. This does not establish exposure safety: wavelength, duration, pulse structure, beam profile, reflections, focusing and viewing optics must be assessed by a qualified laser safety professional.

Why does the calculator sometimes say there is no real result?

A negative square-root expression means no real inverse diameter or divergence exists. For NOHD, an aperture irradiance already at or below the supplied MPE gives an estimated distance of zero. A non-spreading beam above that limit has no finite NOHD in this model.

Is beam divergence entered as full-angle or half-angle?

This calculator uses full-angle beam divergence. If your laser specification gives half-angle divergence, double it before entering the value.