Foot Candle Calculator: Lumens to Foot-Candles

This foot candle calculator converts lumens, distance, and beam angle into foot-candles (fc) or lux, so you can quickly estimate how much light actually reaches a surface. Enter the lamp’s total luminous flux, the distance from the source to the surface, and the beam angle, and you’ll get the illuminance in foot-candles (and lux) at the center of the beam. The result helps you compare lighting layouts, check if a room meets typical illuminance recommendations, or simply understand why a bulb looks brighter up close.

Formula

The calculator uses the inverse-square law for a cone of light. For a source with a total luminous flux \(\Phi\) (in lumens) that emits into a cone with a full apex angle \(\theta\) (in degrees), the illuminance \(E\) at the center of the beam at distance \(d\) is:

\(E = \dfrac{\Phi}{2\pi d^2 \left(1 – \cos\left(\dfrac{\theta}{2}\right)\right)}\)

• \(\Phi\) = total luminous flux (lumens, lm)
• \(d\) = distance from the light source to the surface (feet, ft)
• \(\theta\) = full beam angle (degrees)
• \(E\) = illuminance at the beam center (foot-candles, fc)

To convert foot-candles to lux, multiply by 10.7639 (since 1 fc = 1 lumen per square foot, and 1 lux = 1 lumen per square meter).

Worked Example

Using the default values: \(\Phi = 1000\) lm, \(d = 10\) ft, \(\theta = 60^\circ\).

1. Convert the half-angle to radians: \(\theta/2 = 30^\circ\), so \(\cos(30^\circ) = 0.8660\).
2. Compute \(1 – \cos(30^\circ) = 0.1340\).
3. Compute the denominator: \(2\pi (10^2)(0.1340) = 2 \times 3.1416 \times 100 \times 0.1340 = 84.19\).
4. Divide: \(1000 / 84.19 = 11.88\) fc.

The calculator rounds to one decimal, so it shows 11.9 fc. In lux, that’s \(11.88 \times 10.7639 = 127.8\) lx, which rounds to 128 lx.

What Is a Foot Candle?

A foot-candle is a unit of illuminance: one lumen spread over one square foot. It’s the imperial counterpart to the lux (one lumen per square meter). The term dates back to the era of candles—literally the light of one candle at one foot away. While the name sounds archaic, foot-candles are still widely used in the United States for architectural lighting, photography, and horticulture. Most other countries use lux, but the conversion is simple: 1 fc = 10.7639 lx.

How to Use the Calculator

To get a realistic estimate, you need three pieces of information:

• Total lumens: This is printed on most bulb boxes (e.g., 800 lm for a 60 W equivalent LED).
• Distance: The distance from the bulb to the surface you care about—desk, floor, or plant canopy.
• Beam angle: The spread of the light beam. A standard household bulb might have a beam angle of 60°–120°, while a spotlight could be 15°–30°.

The calculator assumes the surface is perpendicular to the beam and that you are measuring at the brightest spot (the center). For off-center points, illuminance drops off, and the formula becomes more complex.

Common Mistakes and Misconceptions

The most common error is confusing lumens with foot-candles. Lumens describe the total light output of a source; foot-candles describe how much of that light lands on a surface. A 1000-lumen bulb will produce different foot-candle values depending on distance and beam spread. Another frequent mistake is using the diameter of the beam instead of the full angle. The beam angle is the full angle of the cone, not the radius. Also, many people forget that the inverse-square law only applies to point sources; a long fluorescent tube behaves differently, and the calculator will overestimate the illuminance at close range.

Another misconception: “brighter� is not the same as “more foot-candles.� Our eyes perceive brightness logarithmically, so doubling the foot-candles does not look twice as bright. Also, reflective surfaces, walls, and ceilings can increase illuminance in a room beyond the direct-beam calculation, so this calculator gives a conservative estimate for open spaces.

Typical Foot-Candle Recommendations

While this calculator does not provide advice, it helps to know common target ranges so you can interpret the result:

• Living room or bedroom: 10–20 fc (roughly 100–200 lx)
• Kitchen or office work surface: 30–50 fc (300–500 lx)
• Reading or detailed tasks: 50–75 fc (500–750 lx)
• Retail display or jewelry: 100+ fc (1000+ lx)

These are general ranges; actual needs vary with age, task, and personal preference. For horticulture, plants often need 200–1000 fc depending on the species and growth stage.

Limitations of the Formula

The formula assumes a perfect point source with a uniform beam profile. Real bulbs have hot spots, lenses, and reflectors that redistribute light. The result is most accurate for narrow-beam spotlights and distances greater than about 5 times the source diameter. For wide-angle bulbs (like 120°), the center illuminance may be slightly lower than the formula predicts because real beams often have a softer edge. Also, the calculator ignores reflected light, so in a small room with white walls, the actual foot-candles may be higher than calculated.

Frequently Asked Questions

How do I convert foot-candles to lux?

Multiply the foot-candle value by 10.7639. For example, 30 fc × 10.7639 = 322.9 lx. Conversely, divide lux by 10.7639 to get foot-candles.

What is the difference between lumens and foot-candles?

Lumens measure the total light emitted by a source in all directions. Foot-candles measure the light that actually arrives at a surface per square foot. A 1000-lumen bulb with a narrow beam produces more foot-candles at a distance than the same bulb with a wide beam, because the light is concentrated.

Can I use this calculator for LED grow lights?

Yes, as long as you know the total PPF (in µmol/s) or lumens—but note that plants respond to photosynthetically active radiation (PAR), not exactly foot-candles. For a rough estimate, many growers use a conversion factor of about 0.2 µmol/m²/s per lux for white LEDs, but this varies by spectrum.

Why does the calculator show a different value than my light meter?

Light meters measure actual illuminance including reflections and real beam patterns. The calculator gives a theoretical center-beam value. Differences of 10–20% are normal. Also, check that your meter is calibrated and that you are measuring at the same distance and angle.

What beam angle should I use for a standard bulb?

For a typical A19 household LED, the beam angle is often around 120° (wide). For a PAR30 or PAR38 spotlight, it might be 25°–40°. If you don’t know the beam angle, use 120° for general bulbs and 30° for spotlights.

Is 50 foot-candles bright enough for reading?

Yes, 50 fc (about 540 lx) is within the recommended range for reading and detailed work. Many people find 30–50 fc comfortable for a book or craft.

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in lumens | Total luminous flux | lm | 1000 | 0
in dist | Distance from source to surface | ft | 10 | 0
in angle | Beam angle (full width) | deg | 60 | 1
out fc | Illuminance at center | fc | lumens / (2 * pi * dist^2 * (1 - cos(angle / 2 * pi / 180))) | 1
out lux | Illuminance in lux | lx | fc * 10.7639 | 0