Photometric Converter (Lumens ↔ Candela ↔ Lux & Foot-Candles by Beam Angle & Distance)

Convert Lumens, Beam Angle (°), and Distance (m) into Candela (cd), Lux, and Foot-Candles (fc).

Surface Illuminance in Lux (lm/m²)
228.086 lux
Illuminance in Foot-Candles (fc) 21.19 fc
Luminous Intensity in Candela (cd) 1,425.538 cd
Illuminated Spot Diameter at Distance 2.887 m
Inputs
⚡ Scenarios:
lm
Total fixture light output in Lumens (lm).
degrees
Fixture full-width half-maximum beam angle in degrees (10° spot to 120° flood).
m
Perpendicular distance from light source to illuminated surface (m).
Results & Graph
Surface Illuminance in Lux (lm/m²)
228.086 lux
Illuminance in Foot-Candles (fc)
21.19 fc
Luminous Intensity in Candela (cd)
1,425.538 cd
Illuminated Spot Diameter at Distance
2.887 m

Surface Illuminance in Lux (lm/m²)

Graph 1 • Lumens ↔ Lux, Candela & fc • Domain Architecture & Live Telemetry Maps Luminous Flux Lumens, Beam Cone Angle Degrees, Surface Throw Distance Meters through Lumens ↔ Lux, Candela & fc Formula.
ELECTROMAGNETIC & RADIATIO Surface Illuminance in Lux 228.086 lux Illuminance in Foot-Candle 21.19 fc Lumens ↔ Lux, Candela & fc • Component Waterfall Surface Illuminance in Lux (lm 228.086 lux Illuminance in Foot-Candles (f 21.19 fc Luminous Intensity in Candela 1,425.538 cd Illuminated Spot Diameter at D 2.887 m
Graph 2 • Surface Illuminance in Lux (lm/m²) Across Luminous Flux Lumens Sweep (40% → 160%) Evaluates Steradians Ω = 2π × [1 − cos(BeamAngle / 2)]; Candela = Lumens / Ω; across 7 operating points (current input highlighted).
0 lux 200.7 lux 401.4 lux 91.23 480lm 136.9 720lm 182.5 960lm 228.1 1.2klm 273.7 1.4klm 319.3 1.7klm 364.9 1.9klm
Graph 3 • Joint Sensitivity: Luminous Flux Lumens × Beam Cone Angle Degrees Compares Surface Illuminance in Lux (lm/m²) when Beam Cone Angle Degrees is shifted +25% (solid) vs. −25% (dashed).
0 lux 287.0 lux 574.1 lux --- Beam Cone Angle Degrees @ 75% 103.5 -30% 125.7 -15% 147.9 +0% 170.1 +15% 192.2 +30%
Summary: 1200 lm focused into a 60° beam (0.842 sr) produces 1426 Candela and 228.1 Lux (21.2 foot-candles) at 2.5 m across a 2.89 m beam circle.
Summary: 1200 lm focused into a 60° beam (0.842 sr) produces 1426 Candela and 228.1 Lux (21.2 foot-candles) at 2.5 m across a 2.89 m beam circle.
⚡ Send result to: Unit Converter →Scientific →Date Difference →
Interactive chart & math engine powered by CalculatorGraph

Formula & Mathematical Methodology: Lumens ↔ Lux, Candela & fc Formula

Steradians Ω = 2π × [1 − cos(BeamAngle / 2)]
Candela = Lumens / Ω
Lux = Candela / Distancem²
FootCandles = Lux / 10.7639
Steradians Ω = 2π × [1 − cos(BeamAngle / 2)]; Candela = Lumens / Ω; Lux = Candela / Distance_m²; FootCandles = Lux / 10.7639
  • luminousFluxLumens: Total fixture light output in Lumens (lm).
  • beamConeAngleDegrees: Fixture full-width half-maximum beam angle in degrees (10° spot to 120° flood).
  • surfaceThrowDistanceMeters: Perpendicular distance from light source to illuminated surface (m).

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Lumens ↔ Lux, Candela & fc Worked Example

Convert Lumens, Beam Angle (°), and Distance (m) into Candela (cd), Lux, and Foot-Candles (fc).

  1. Enter the input measurement, system configuration, or astronomical parameter.
  2. Apply the standard conversion or analytical equation: Steradians Ω = 2π × [1 − cos(BeamAngle / 2)]; Candela = Lumens / Ω; Lux = Candela / Distance_m²; FootCandles = Lux / 10.7639.
  3. Inspect the primary metric, secondary equivalents, and 3 real-time SVG graphs.
Result: Computes Lumens ↔ Lux, Candela & fc via Steradians Ω = 2π × [1 − cos(BeamAngle / 2)]; Candela = Lumens / Ω; Lux = Candela / Distance_m²; FootCandles = Lux / 10.7639.

Frequently Asked Questions

How does the Photometric Converter (Lumens ↔ Candela ↔ Lux & Foot-Candles by Beam Angle & Distance) perform the calculation?

It evaluates Steradians Ω = 2π × [1 − cos(BeamAngle / 2)]; Candela = Lumens / Ω; Lux = Candela / Distance_m²; FootCandles = Lux / 10.7639 directly in your browser and renders three custom SVG charts in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this tool work offline?

Yes. All calculations run 100% locally in your browser with full offline PWA support.

Unit Conversions · Electromagnetic & Radiation Conversions

Photometric Converter (Lumens ↔ Candela ↔ Lux & Foot-Candles by Beam Angle & Distance): inputs, method, and how to read the result

Convert Lumens, Beam Angle (°), and Distance (m) into Candela (cd), Lux, and Foot-Candles (fc).

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Luminous Flux Lumens: Total fixture light output in Lumens (lm).
  • Beam Cone Angle Degrees: Fixture full-width half-maximum beam angle in degrees (10° spot to 120° flood).
  • Surface Throw Distance Meters: Perpendicular distance from light source to illuminated surface (m).

What the calculation includes

With the default values shown, Surface Illuminance in Lux (lm/m²) is 228.086 lux. The calculation follows Lumens ↔ Lux, Candela & fc Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Luminous Flux Lumens from 1,200 lm to 1,320 lm changes Surface Illuminance in Lux (lm/m²) from 228.086 lux to 250.895 lux. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses official NIST Special Publication 811, IEEE/RFC systems engineering, APA psychometric, and USNO astronomical formulas.
  • Empirical metallurgy and calendar conversions represent standard reference-condition approximations.

Scope: Global NIST, IEEE, APA & Astronomical Standard Check the assumptions and limitations against your situation before relying on the estimate.

More in Unit Conversions: Unit Conversion Calculator, Scientific Calculator, Date Difference & Business Days Calculator.