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A comprehensive resource for safe and responsible laser use
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Beam Diameter and Irradiance Calculator
If you know the power and divergence of a visible, continuous wave laser, you can use the online calculator below to find out the beam diameter and irradiance at a given distance. The calculator also includes results for the Nominal Ocular Hazard Distance, beyond which the beam is considered to be safe for direct viewing.
- The calculator does not work using Internet Explorer. All answers will be “.000”. Please use a different browser. If you continue to have problems, contact us.
- For a full-featured Laser Hazard Distance Calculator, with the NOHD, ED50, and FAA visual interference distances, click here.
Beam Diameter and Irradiance Calculator
This calculator is valid only for lasers emitting visible (400-700 nanometers), continuous wave (CW) laser light, over long distances.
mW
Enter the laser’s power in milliwatts.
If you know the power in watts, multiply the watts by 1000 to get milliwatts. For example, for a 1 watt laser, enter 1000; for a 1.5 watt laser, enter 1500; for a 40 watt laser enter 40000.
If you know the power in watts, multiply the watts by 1000 to get milliwatts. For example, for a 1 watt laser, enter 1000; for a 1.5 watt laser, enter 1500; for a 40 watt laser enter 40000.
mrad
If you don’t know the beam divergence, use 1 milliradian for lasers under 500 milliwatts in power, and 1.5 milliradians for lasers 500 milliwatts and above.
units
Enter the distance from the laser output to the target or other desired distance. Just enter the distance number. Then use the drop-down list below to tell the calculator which distance unit you’re using: meters, kilometers, feet, miles, or nautical miles.
Results are below, in black. The beam diameter and NOHD results use the distance unit selected above. Results are continuously updated as you enter new information — you do not have to click a “=“ or “Calculate” button.
[dist]
*
[units]
0
(([mrad]/1000)*[dist-in-meters])+.001
Beam diameter result
A Gaussian laser beam is brightest in the center, and gradually falls off to the edges. The diameter listed here is the area where 63% of the beam power is contained, called the “1/e width.”
Specifically, “the distance between diametrically opposed points in that cross section of a beam where the power per unit area is 1/e (0.368) times that of the peak power per unit area.” This definition comes from the laser safety standard ANSI Z136.1.
Specifically, “the distance between diametrically opposed points in that cross section of a beam where the power per unit area is 1/e (0.368) times that of the peak power per unit area.” This definition comes from the laser safety standard ANSI Z136.1.
.000
[beam-diameter]
NOTE: If all results are “.0000”, then the calculator does not work with your browser, which is probably Internet Explorer. Please use a different, up-to-date browser.
Irradiance result
Irradiance is the power of the laser, spread out over an area. Because laser beams diverge, the irradiance will be higher (more hazardous) closer to the laser, and will be lower (less hazardous) farther from the laser.
.000 mW/cm²
[mw]
/
(
(
[beam-diameter]
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[beam-diameter]
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7854
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Click for more details
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About Gaussian beams
- Most laser beams used in pointers and light shows are Gaussian. This means they are brightest in the center and they fall off towards the edges. The center is the “worst case” area for an eye to be located.
The irradiance calculation above takes this into account by using the 1/e width of the beam. FDA, FAA and ANSI all use this technique for reporting and analyzing irradiance.
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Gaussian profile compared with top hat profile
- A Gaussian beam has a center brightness roughly twice that of a top hat profile where the irradiance is constant across the beam, falling quickly to zero. This is shown below:
So first we find the average irradiance across the beam diameter at the 1/e points as per ANSI Z136.1, which gives the irradiance for a smooth top hat profile. Then we multiply by two to get the irradiance for the center of a Gaussian beam.
Use this “2x” value for safety calculations. It is the “worst case” — if a person’s pupil is in the center of the beam. -
Maximum allowed irradiance values (MPEs)
- These are the values for the Maximum Permissible Exposure, for eye exposure to visible continuous wave laser light. These are the maximums; you are not allowed to exceed this value, for the exposure duration listed.
- 0.251 - 1 second: 1.8 mW/cm2
- 0.011 - 0.25 second: 2.54 mW/cm2. This value is used for accidental, unwanted exposure to visible light, where a person is expected to blink and/or turn away within 1/4 second of experiencing a bright light.
- 0.0011 - 0.01 second: 5.6 mW/cm2
- 18.1 microseconds - 0.001 second: 10 mW/cm2
- 18 microseconds or less: 27 mW/cm2
For longer exposures such as 10 seconds, 10 minutes and 8 hours, the MPE is wavelength dependent. For example, the MPE for a 10 minute exposure to red 633 nm laser light is 0.253 mW/cm2; for blue-green 514 nm laser light it is 0.0167 mW/cm2.
These values come from the laser safety standard ANSI Z136.1. -
To convert mW/cm2 to W/cm2 or W/m2
- In the U.S., milliwatts per square centimeter is most commonly used. But in Europe and elsewhere, watts per square centimeter or watts per square meter is often seen.
Milliwatts per square centimeter <-> Watts per square centimeter- To convert mW/cm2 to W/cm2, divide by 1000. For example, 2.54 mW/cm2 equals 0.00254 W/cm2.
- To convert W/cm2 to mW/cm2, multiply by 1000. For example, 0.00254 W/cm2 equals 2.54 mW/cm2.
Milliwatts per square centimeter <-> Watts per square meter- To convert mW/cm2 to W/m2, multiply by 10. For example, 2.54 mW/cm2 equals 25.4 W/m2.
- To convert W/m2 to mW/cm2, divide by 10. For example, 25.4 W/m2 equals 2.54 mW/cm2.
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If your results don’t match…
- If you do laser safety calculations using different sources, you might find that results from one calculator or equation or computer program might not exactly match up with results from another.
Generally, if the results are within about 5% or less of each other, this is OK. To be on the safe side, use the value that is more conservative.
For example, if one calculator says the NOHD of a particular laser is 560 meters, and another says it is 567 meters, use the longer distance (further from the laser and thus safer).
Why results can vary
Results can vary due to using slightly different values for certain constants. For example, the MPE for a 1/4 second exposure might be 2.5, 2.54 or 2.55 mW/cm2 depending on the calculator or equation source.
Or, a factor such as the initial width of the beam may be ignored when calculating safety distances many meters from the laser aperture, since it has little effect over long distances.
Finally, safety concepts such as the NOHD etc. are not exact. If a calculator determines the NOHD is “567.5 meters”, this does NOT mean that your eyes will be damaged at 567.4 meters but will be safe at 567.6 meters.
Rounding is OK
In fact, saying the NOHD is “567.5” gives a false impression of precision. In this case it would be fine to round up the NOHD (make it slightly longer) to 570 meters.
Note: The calculator on this page does not round because the underlying code cannot handle sophisticated rounding. Results are always given to 3 decimal places because sometimes we need the decimal places (“0.051”) even though many times we don’t (“3,271.103” is just too precise!).
Eye hazard result
The NOHD distance depends only on the power and divergence of the laser. It does not depend on the distance that you entered above.
Starting at the NOHD distance, laser light directly entering the eye is at the Maximum Permissible Exposure (MPE) and is generally considered safe. Specifically, at the NOHD there is “a negligible probability of damage” according to the laser safety standard ANSI Z136.1.
The farther one gets from the NOHD, the lower the irradiance, meaning that the light is even safer.
Starting at the NOHD distance, laser light directly entering the eye is at the Maximum Permissible Exposure (MPE) and is generally considered safe. Specifically, at the NOHD there is “a negligible probability of damage” according to the laser safety standard ANSI Z136.1.
The farther one gets from the NOHD, the lower the irradiance, meaning that the light is even safer.
.000
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32.8
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[mrad]
)
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(
sqrt
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0.5
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[mw]
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0.3048
/
[units]
Compare with the beam diameter/irradiance distance you entered above. If the NOHD is greater than the distance entered above, then there is an eye safety hazard (if a person’s eyes are allowed to view laser light at the distance entered above).
.000
[dist]
For a full-featured Laser Hazard Distance Calculator, with the NOHD, ED50, and FAA visual interference distances, click here.
SAFETY NOTICE: The calculator above is intended for the educational, instructional and informational purposes of the user and is not to be considered a substitute for a knowledgeable and trained Laser Safety Officer (LSO) with the duties and responsibilities as defined in the ANSI Z136 standard. Consult with an LSO for safety-critical usage or special cases. While care has been taken to ensure accurate calculations, we are not responsible for errors. (If you do find errors please contact us with details.)
Additional laser hazard calculators
For a full-featured Laser Hazard Distance Calculator, with the NOHD, ED50, and FAA visual interference distances, click here.
We also have information about other calculators and dedicated programs. These can analyze complex situations involving multiple simultaneous colors, pulsed lasers, non-visible lasers, and/or atmospheric attenuation.
If you are a member of the International Laser Display Association, you can use ILDA’s free online Skyzan professional laser hazard calculator.
We also have information about other calculators and dedicated programs. These can analyze complex situations involving multiple simultaneous colors, pulsed lasers, non-visible lasers, and/or atmospheric attenuation.
If you are a member of the International Laser Display Association, you can use ILDA’s free online Skyzan professional laser hazard calculator.