Sizu Riatto
Grow by Numbers · Chapter 8

Light: the Square Law

Raise a light and the tray gets less. How much less depends on the shape of the light: a point source follows the inverse square, a long bar close up falls nearer 1/d. Two phone readings tell you which you have.

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Opens on the book's Microgreen Shelf. Change any number to your own and press Calculate.

The light at the tray

Your phone's light meter: two readings (optional)

Power and cost

Enter the heights and the lights, then press Calculate.

The formula

  • A long bar close up: light ∝ 1/d, so the share left = old height ÷ new height
  • A point source: light ∝ 1/d², so the share left = (old ÷ new)²
  • Your own light: light ∝ dⁿ with n = log(reading 2 ÷ reading 1) ÷ log(height 2 ÷ height 1)
  • kWh a day = watts × lights × hours ÷ 1,000; cost = kWh × your price
  • Per tray a day = kWh a day ÷ trays; a crop's tray = that × its days on the shelf
The book's worked example, Chapter 8. The shelf's four 40 W bars hang 25 cm (about 10 in) above the trays. Raised to 35 cm they leave about 71% (long bar, 1/d) or 51% (point, 1/d²). Readings of 2,400 and 1,300 lux give n = -0.88, so 35 cm leaves 74.3%. Power: 2.56 kWh a day, 76.8 kWh in 30 days, 0.32 kWh per tray a day; a radish tray's 9 days cost 0.52 at 0.18 a kWh.
Check it. Halve the height on paper: a point source should give four times the light, a long bar about twice. Your readings' n should sit between −1 and −2 or near −1.

Honest limits. A phone's lux meter reads light for human eyes, not plant light (PPFD): use it only to compare heights with the same light. Rated watts are what the label says; a plug-in meter tells you the draw. The Microgreen Shelf was worked out on paper from published figures, not grown by us: weigh and measure your own. Prices are illustrative US prices from October 2026, shown without a currency sign; put in your own. Everything stays in your browser: no sign-up, nothing stored.

These calculators go with Grow by Numbers (Make It Add Up, Book 1), where every number on this page is worked by hand.