Why is inverse square wrong for a UV lamp?

Because inverse square describes a point source, and it only applies once you are far enough away that the source looks like a point: conventionally about five times its largest dimension. A ten-inch arc would need fifty inches of standoff to qualify, and UV curing works at one to six. At those distances a tube behaves much more like a line source, whose field falls as 1/d. The instinct is imported from optics where sources really are small, and it does not survive the geometry here.

How big is the error in practice?

The ratio of the two predictions is exactly the distance ratio. A move from 2 inches to 3 gives 800 mW/cm² under the line law and 533 under inverse square: 50% apart. A move from 2 to 4 gives 600 against 300, a factor of two. Since every dose calculation is linear in irradiance, that error passes straight through to belt speed, exposure time and cure margin.

So which number should I use?

The one the page selects for your regime, treated as the middle of a bracket rather than an answer. A real tube is neither an ideal line nor an ideal point, so the truth sits between the two predictions, closer to the line law at short distances and drifting toward inverse square as you back off. Where the decision matters, put a radiometer at the new distance: the whole spread disappears the moment you measure.

What about focused reflector systems?

Neither law describes them near focus, and this is the page's biggest limitation. A focused system concentrates irradiance at a focal plane, so irradiance rises as you approach that plane and falls on either side of it. Moving a part closer to the lamp can therefore reduce irradiance, which no monotonic falloff law can express. If your system has a stated focal distance, treat that as the operating point and measure any departure from it.

Why did the earlier version ask for a factor instead of the distances?

It should not have, and that is the first of this page's two defects. Asking for the inverse-square factor requires the user to compute (d_ref/d_new)² themselves. The answer supplied as an input, and it silently commits them to the wrong law at the same time. Asking for the two distances and the arc length lets the page do both the arithmetic and the physics, and lets it show its working.

Does moving the lamp away have any upside?

Yes, and it is why people do it besides clearing tall parts. Irradiance falls but uniformity improves: further from the source the profile flattens across the part, both along the belt and across its width. For a shaped part with faces at different distances, a longer standoff can deliver a more even dose even though it delivers less of it. The uniformity and dose-mapping pages measure that trade.

UV Curing calculator

UV Lamp Distance Intensity Calculator (Line vs Point Source)

Work out what moving a UV lamp does to the irradiance at the part. Enter the measured irradiance and the distance it was measured at, the distance you are moving to, and the lamp's arc length. The calculator returns predictions under both falloff laws and tells you which one applies, because the answer depends on which regime you are in, and for arc-lamp UV curing that is almost never the one people assume. The lamp's arc length is here because the ratio between it and the working distance is what decides the regime.

What this calculator does

Predict what moving a lamp does to irradiance at the part, using the falloff law that actually applies to a tube rather than assuming inverse square.
Use it for predicting what raising a lamp to clear a taller part does to cure, deciding whether a fixed lamp height can serve two part heights, explaining why a lamp move cost less irradiance than inverse square predicted, bracketing the irradiance at a distance you cannot get a radiometer to, checking whether a proposed standoff still clears a minimum irradiance requirement.
Predict what moving a lamp does to irradiance at the part, using the falloff law that actually applies to a tube rather than assuming inverse square.

Formula used

Distance ratio = reference distance ÷ new distance
Line-source prediction = baseline × (distance ratio)¹
Point-source prediction = baseline × (distance ratio)²
Far field begins at new distance ≥ 5 × arc length
Predicted irradiance = point-source prediction in the far field, line-source otherwise
Spread = |line-source prediction − point-source prediction|

Inputs explained

Baseline irradiance at reference distance: Measured irradiance at the distance you are moving away from.
Reference distance: Lamp-to-part distance at which the baseline irradiance was measured.
New distance: Lamp-to-part distance you are moving to.
Lamp arc length: Length of the illuminated arc. This decides which falloff law applies: below about five arc lengths the tube behaves as a line source, not a point.

How to use the result

Best suited to predicting what raising a lamp to clear a taller part does to cure, deciding whether a fixed lamp height can serve two part heights, explaining why a lamp move cost less irradiance than inverse square predicted, bracketing the irradiance at a distance you cannot get a radiometer to, checking whether a proposed standoff still clears a minimum irradiance requirement.
A focused reflector system has a focal plane and does not obey either law near it; moving closer can reduce irradiance. Neither prediction here describes that. The five-arc-length boundary is a rule of thumb, not a physical edge, so predictions near it are least reliable. Real tubes are neither perfect lines nor points, so the true answer sits between the two predictions rather than on either. Ignores the angle of incidence, which matters for a part that is not flat and normal to the lamp. Says nothing about uniformity. Moving a lamp away flattens the profile as well as dimming it, which is sometimes the reason to do it.

Common questions

Why is inverse square wrong for a UV lamp? Because inverse square describes a point source, and it only applies once you are far enough away that the source looks like a point: conventionally about five times its largest dimension. A ten-inch arc would need fifty inches of standoff to qualify, and UV curing works at one to six. At those distances a tube behaves much more like a line source, whose field falls as 1/d. The instinct is imported from optics where sources really are small, and it does not survive the geometry here.
How big is the error in practice? The ratio of the two predictions is exactly the distance ratio. A move from 2 inches to 3 gives 800 mW/cm² under the line law and 533 under inverse square: 50% apart. A move from 2 to 4 gives 600 against 300, a factor of two. Since every dose calculation is linear in irradiance, that error passes straight through to belt speed, exposure time and cure margin.
So which number should I use? The one the page selects for your regime, treated as the middle of a bracket rather than an answer. A real tube is neither an ideal line nor an ideal point, so the truth sits between the two predictions, closer to the line law at short distances and drifting toward inverse square as you back off. Where the decision matters, put a radiometer at the new distance: the whole spread disappears the moment you measure.
What about focused reflector systems? Neither law describes them near focus, and this is the page's biggest limitation. A focused system concentrates irradiance at a focal plane, so irradiance rises as you approach that plane and falls on either side of it. Moving a part closer to the lamp can therefore reduce irradiance, which no monotonic falloff law can express. If your system has a stated focal distance, treat that as the operating point and measure any departure from it.
Why did the earlier version ask for a factor instead of the distances? It should not have, and that is the first of this page's two defects. Asking for the inverse-square factor requires the user to compute (d_ref/d_new)² themselves. The answer supplied as an input, and it silently commits them to the wrong law at the same time. Asking for the two distances and the arc length lets the page do both the arithmetic and the physics, and lets it show its working.

Last reviewed 2026-08-25.