Why a Grow Light's Coverage Area Needs a Height

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Far less often than the inverse square law makes you think, and the reason is that the inverse square law is the wrong law. A panel is not a point source at the heights people hang it, and the difference between the two is a factor of 2.7 on the question you are asking.

Here is the shape of the real answer. Raising a 1 by 2 foot panel from 6 inches to 18 inches above the canopy removes 70 percent of the light. An inverse square law predicts 89 percent. And a published coverage area of 2 by 3 feet, which is the only coverage figure in our catalogue, corresponds to a mounting height of anywhere between 3.46 and 10.39 inches depending on a beam angle no grow light here publishes. A coverage area with no height on it is half a specification.

From a watt to something a plant answers

A MetryGrow 100W smart LED grow light is the right product to start on because it is unusually straight about the one figure it gives. Its record makes the point explicitly: "Grow lights are notorious for exaggerated wattage claims. MetryGrow makes a point that this is a genuine 100 watt LED, not an inflated figure." It publishes a stated 2 by 3 foot coverage, full spectrum output, app control, aluminium honeycomb cooling and daisy-chain support, and it is upfront that no stand or mounting kit comes with it.

An honest wattage is better than a dishonest one and it is still only the first link in a chain of three. Watts go in. Photons come out at some efficacy. Those photons land on some area. And the plant responds to a number of photons per square meter per second, accumulated over a photoperiod.

Take a modern white horticultural LED at a representative 2.2 micromoles of photosynthetic photons per joule. One hundred watts is then 220 micromoles a second of photon flux. Spread over the published 2 by 3 feet, which is 6 square feet or 0.5574 square meters, that is 394.7 micromoles per square meter per second.

Run it for 16 hours and the daily total is 394.7 times 57,600 seconds, which is 22.73 moles per square meter per day. The conventional bands are 12 to 17 for seedlings and leafy greens and 20 to 30 for fruiting crops, so over its stated footprint this light genuinely reaches the fruiting band. At a 12 hour photoperiod the same fixture delivers 17.05 moles, because the photoperiod multiplies the whole chain directly.

That is a good light. It is also a result that depends completely on the footprint, and the footprint depends completely on the height.

The law that is not inverse square

A point source radiates into a solid angle and its intensity falls as one over the distance squared. Our page on whether more lumens mean a light shines further works that chain out properly for a beam, and this page takes it rather than repeating it.

A panel is different, and the difference is geometric rather than subtle. The lit area under a rectangular panel of width W and length L at a standoff d, with a beam half angle of theta, is W plus twice d times the tangent of theta, multiplied by L plus the same quantity. Both terms are linear in d. So the area grows as the product of two linear terms, and the flux density goes as one over that product.

When d is small compared with W and L, the added terms barely matter and the intensity is nearly flat with height. When d is large compared with the panel, the panel's own dimensions drop out and the expression collapses to one over four d squared tangent squared theta, which is the inverse square law. The familiar law is the asymptote, not the rule.

Put the numbers on it. For a 1 by 2 foot panel at a 45 degree half angle:

At 6 inches the footprint is 0.6096 by 0.9144 meters, which is 0.5574 square meters, and the flux density is 394.7.

At 12 inches it is 0.9144 by 1.2192, which is 1.1146 square meters, and the density is 197.4. Exactly half, for doubling the height.

At 18 inches it is 1.2192 by 1.5240, which is 1.8581 square meters, and the density is 118.4, so 30.0 percent of what you started with.

An inverse square law from 6 to 18 inches would have left 394.7 divided by 9, which is 43.9. The real figure is 118.4. The law everyone reaches for understates what survives by a factor of 2.70, and it does so in the direction of making people too nervous about height.

And the asymptote arrives nowhere useful. For the inverse square approximation to be within 20 percent on this panel you need a standoff of about five feet, which is ten times the height the light is designed for.

The height hidden inside a coverage area

Now run that backwards, because it answers the question the listing leaves open.

For a footprint to come out as 2 by 3 feet, the growth has to be the same in both directions, which means the panel itself is one foot longer than it is wide. So twice the height times the tangent of the half angle equals one foot, which is 0.3048 meters.

At a 30 degree half angle that gives a height of 0.2640 meters, which is 10.39 inches. At 45 degrees it gives 0.1524 meters, which is 6.00 inches. At 60 degrees it gives 0.0880 meters, which is 3.46 inches.

A factor of three in the single number the buyer has to set with their own hands, decided by a beam angle that no grow light in this catalogue publishes. The record knows this matters and says so twice: "You must arrange your own way to hang or mount it at the right height above the plants", and "Getting that height and the daily light schedule right for each plant type matters for good growth." Both sentences are correct. Neither is actionable without a number.

This is the same gap, in the same shape, as the one our page on why blender rpm needs a blade diameter describes: a figure that looks like a specification and cannot be compared with anything because the other half of the pair is missing. There, an rpm with no diameter. Here, a coverage area with no height, and a wattage with no efficacy.

Our own guide to growing plants indoors with grow lights gets the direction exactly right, and it deserves the credit for being blunt about the wattage problem before anyone else: "grow-light wattage is often wildly exaggerated", and "Too close can stress or scorch plants; too far and the intensity drops off." The arithmetic above is what those two sentences are worth in micromoles.

What the daisy chain is actually for

The same listing publishes "seamless daisy-chaining" and treats it as a convenience feature about plugs. It is not. It is the only way to add light without giving any up.

Flux density is total photon flux divided by lit area. So two lights side by side at 6 inches cover 2 by 6 feet and still deliver 394.7, because the flux doubled and so did the area. One light raised until it covers that same 12 square feet delivers 220 divided by 1.1148, which is 197.3. Exactly half.

Chaining holds the density constant as the garden grows. Raising divides it. That is a factor of two for the same footprint, it is exact, and it appears on the listing as a tidiness feature. Our roundup of plant grow lights for thriving indoor plants is the place to compare fixtures, and this is the question to carry into it: how many does the shelf need, rather than how high does one go.

A bead count is not a photon flux

A Patigrow 120-cell self-watering seed starter kit publishes a great deal and publishes it carefully: 120 cells across two separate 60-cell trays, capillary self-watering, four LED strips with 56 beads per tray, adjustable brightness with timer functions, domes 4.07 inches tall with two adjustable vents each, 1.5 mm BPA-free PET, a kit 16.6 by 11 by 7.28 inches weighing 3.8 pounds, and plant stands "to set the trays at the right distance from the lights".

Everything in that list is a figure except the one that matters for light. A bead count is not a flux, and the gap it leaves is enormous.

Strip LEDs of this kind draw somewhere between 0.2 and 0.5 watts each. Fifty six of them is therefore 11.2 to 28 watts, which is already a factor of 2.5. Push that through an efficacy band of 1.0 to 2.2 micromoles per joule, because small 5 volt beads sit well below the 2.2 a dedicated panel manages, and the photon flux is 11.2 to 61.6 micromoles a second. A factor of 5.5.

One 60-cell tray in that kit is roughly 8.3 by 11 inches, so 0.0589 square meters. At the bottom of the band that is 190 micromoles per square meter per second, which at 16 hours is 10.9 moles a day, just under the seedling floor. At the top it is 1,046, which is 60.3 moles a day and ample for anything. The published number cannot tell those two situations apart, and the kit publishes no wattage at all.

What the kit does get right is the mechanism for adjustment, and it is the better one. Instead of a hanging height you have to keep changing, it includes plant stands to raise the tray toward the light. That is thermodynamically identical and mechanically far easier, because a tray with a handle moves and a light screwed to a shelf does not. It is the correct answer to the question at the top of this page and it arrives without any arithmetic attached.

The dome that takes two thirds of your height

There is one more number in that kit worth pulling out, because it constrains the thing the whole page is about. The humidity domes stand 4.07 inches tall. That is 103.4 millimeters of mandatory standoff between the light and the seed for as long as the dome is on.

Against the 152.4 millimeters the coverage arithmetic implied at a 45 degree half angle, the dome is 67.8 percent of the entire recommended height. The grower has about 49 millimeters of discretion and the lid has the rest.

Which reframes the vents, correctly, as a lighting feature as much as a humidity one. The record is sharp about when they matter: the domes "trap warmth and moisture for germination, and the two adjustable vents per dome let you reduce that as seedlings emerge, which is when trapped humidity turns from help to hazard". Taking the dome off at that point does not only drop the humidity. It returns two thirds of your height budget, and on the arithmetic above that is worth roughly a doubling of flux density at the leaf.

A Kokopro seed starter kit with grow lights and heat mat publishes "heightened humidity domes" with no figure, so the same fraction cannot be formed for it, and heightened is the direction that makes it worse rather than better.

An ambiguity in our own record that its own numbers settle

That Kokopro kit publishes a far-infrared heat mat holding 70 to 85 Fahrenheit with double insulation layers and an IP67 rating, three trays, three grow lights, an intelligent controller with four timing settings, cells in "equal 1.96 inch squares at 1.85 inch depth", and a kit measuring 10.2 by 8.07 by 6.69 inches.

Its own record then flags something it could not resolve: "The title states 36 extra large cells and describes a three pack, and the bullets do not clarify whether 36 is the count per tray or the total across all three. We have reported both readings rather than pick one."

Both readings cannot stand, and the listing's own dimensions settle it. A cell 1.96 inches square is 3.8416 square inches. Thirty six of them is 138.3 square inches. The published tray footprint is 10.2 by 8.07 inches, which is 82.31 square inches. Thirty six cells per tray would need 1.68 times the whole tray, walls and rim included, which is impossible.

So 36 is the total, which is 12 cells per tray. Twelve cells at 3.8416 is 46.1 square inches, which is 56.0 percent of the footprint and leaves a sensible allowance for dividing walls and a lip. The open question in our own record has an answer sitting in two other fields of the same record.

Twelve cells per tray also changes what the kit is for, which is why it was worth doing. Thirty six large cells across three trays is a modest sowing with generous root room, exactly matched to the crops the mat exists for, and the record is right about why those crops need it: "Soil temperature, not air temperature, is what triggers them." That sentence is correct and it is the best thing on the listing.

What cannot be checked is the trade between the kit's two heat paths, because only one of them has a figure. Essentially the entire electrical input of an LED fixture ends up as heat, the photons included once they are absorbed, so a 100 watt grow light is also a 100 watt heater, delivered from above into the air and the leaves. The mat delivers its heat from below into the medium, where the record correctly says the trigger is. No mat wattage is published, so the only honest statement is that the kit contains two heaters pointing in opposite directions and publishes a temperature range for one of them. Our roundup of seedling heat mats for faster germination is the place to compare the mats on their own terms.

The only published photon figure, and the unit problem beside it

A SEAOURA WRGB aquarium LED light is the one product in this catalogue that publishes anything resembling a photon measurement, and it publishes it in a crowd: "CRI 93, PAR 89, 2142 lumens, 10000K, and 22W, with enhanced 455nm blue and 660nm red for photosynthesis", on 90 chips in a four-channel layout for 18 to 24 inch tanks.

Start with the honest part, because the record flags it itself: "PAR and lumen figures are maker-stated" and "Growth varies with tank depth". Both true, and the second one is the key to the first.

A bare "PAR 89" has no unit and no distance. If it is a flux density in micromoles per square meter per second, the question is where, and tank depth is exactly the variable the record names. Work it from the lumen figure instead. At a luminous efficacy of radiation near 300 lumens per radiometric watt for a cool white source, 2142 lumens is about 7.14 watts of radiant power, and a mole of 550 nanometer photons carries 217.7 kilojoules, so that is 32.8 micromoles a second. On the published 22 watts that is 1.49 micromoles per joule, which is modest for horticulture and reasonable for a fixture spending part of its budget on colour channels.

Spread 32.8 micromoles a second over a 20 by 10 inch tank surface, which is 0.1290 square meters, and you get 254 micromoles per square meter per second at the water line, against a published PAR of 89. A factor of 2.9. The two figures are not inconsistent. They describe the light in two different places, and the listing names neither of them. Our guide to lighting a planted aquarium says that demanding plants "need high PAR and penetration", which is right, and the figure that would make it usable is a flux density with a depth attached.

Why a lumen is the wrong unit, with the factor

And then there is the deeper problem with publishing a lumen figure on a fixture sold for photosynthesis, which is that the two quantities disagree about which photons count.

A lumen is radiant power weighted by the human eye's photopic response, which peaks in the green at 555 nanometers. That response is about 0.04 at 455 nanometers and about 0.061 at 660, against 1.00 at the peak. A photon flux density counts every photon between 400 and 700 nanometers equally.

So a 455 nanometer blue photon contributes roughly a twenty-fifth as much to a lumen total as a green one, and a 660 nanometer red photon roughly a sixteenth, while all three are worth the same to a plant. Which means that the fixture's own headline feature, "enhanced 455nm blue and 660nm red for photosynthesis", pushes its lumen number down. Every photon moved out of the green and into the bands plants use most is a photon that nearly vanishes from the lumen count.

That is why no amount of care with a lumen figure makes it a horticultural number, and it is the arithmetic behind the standing advice never to shop for a grow light on lumens. It also explains a question people keep asking about 20,000 kelvin bulbs and the like: a colour temperature describes the shape of a white spectrum as the eye sees it, and two sources with the same figure can differ substantially in how many photons they put in the red.

One tension inside that same product's numbers, worth noting rather than overstating. CRI 93 measures how faithfully a source renders colours against a blackbody reference, and strongly peaked red and blue spectra usually score poorly on it. A four-channel fixture with a dominant white channel can honestly do both, but then the enhancement of the two narrow bands has to be modest. Either the boost is small or the CRI was measured with the channels set differently from a growth setting, and the listing does not say which.

What a windowsill is, numerically

A HOME GROWN indoor herb garden starter kit is worth including precisely because it has no light in it, and its own drawbacks are honest about the consequence: "Grows from seed, needs light and patience", and "Results vary with light and care". Both sentences are correct and both are doing a lot of quiet work.

Here is roughly what they mean. A bright south-facing sill in winter at middle latitudes receives something like 1 to 4 moles per square meter per day, once the glass, the window's restricted view of the sky and the short day are accounted for. The seedling floor is around 12. So a windowsill in January is somewhere between three and twelve times short, which is not a deficit that patience fixes.

The 100 watt panel at the top of this page, over its own footprint at 16 hours, delivers 22.73 moles. That is roughly six to twenty times a winter sill. Which is the honest version of the sentence every grow light listing opens with, and the reason the kits that include a light are a different proposition from the ones that do not. Our roundup of grow light stands for healthy indoor seedlings covers the mounting problem that the panel's own record declines to solve.

The honest limit, and the answer to the question

Three things on this page are exact. The footprint of a panel grows as the product of two linear terms, so the inverse square law is its asymptote and not its rule, and the 2.70 discrepancy at 18 inches follows from geometry alone. Flux density is total flux over area, so the daisy chain's factor of two is arithmetic. And the daily light integral is a flux density times a number of seconds. The 56 percent of the Kokopro tray and the impossibility of 36 cells per tray are also exact, being two published dimensions multiplied together.

One input is load-bearing and representative, and it is the efficacy. Not one grow light in this catalogue publishes a micromoles per joule, a photon flux, or a flux density with a distance attached, so the 2.2 is a reasonable figure for a modern white horticultural LED and nothing more. At 1.8 the first panel reads 323 micromoles per square meter per second and 18.6 moles a day. At 2.8 it reads 502 and 28.9. Every ratio and every percentage on this page is untouched by that choice, and every absolute figure scales with it.

Also representative: the 1 by 2 foot panel geometry, which was deduced from the published aspect of the coverage rather than stated; the 0.2 to 0.5 watts per strip bead; the 300 lumens per radiometric watt used to turn a lumen figure into photons; the windowsill estimate, which no product could publish; and the 12 to 17 and 20 to 30 mole benchmark bands, which are conventional horticultural numbers rather than anything a listing says.

What this page deliberately does not compute is a plant outcome. Turning a daily light integral into a growth rate needs a species, a temperature, a carbon dioxide concentration and a light response curve that saturates, and nothing in this catalogue publishes any of them. Nor has it computed a spectrum effect beyond the lumen weighting, because that would need a channel-by-channel photon distribution and the only fixture that publishes a wavelength publishes two of them with no proportions.

And the answer to the question, which was whether adjusting the height is worth the hassle. On the arithmetic: between 6 and 12 inches you are trading a factor of two in intensity for a factor of two in area, which is a real decision and not a small one. Above about a foot the curve has already given away 70 percent and keeps going. Below the dome you have no choice at all until the dome comes off, and taking it off at the right moment is worth about as much as any height adjustment you will ever make. If the fixture can be chained, chain it instead of raising it, because that is the one move with no cost in intensity. And if you are going to adjust anything weekly, adjust the tray rather than the light, which is what the one kit here that thought about it already does.