Candela to Lumens Calculator

Candela to Lumens Calculator

Common beam angles: 120° for floodlights, 15-40° for spotlights.

Total Luminous Flux:

---

Understanding the Candela to Lumens Conversion

Converting candela to lumens is essential for lighting designers, photographers, and engineers who need to understand how light intensity translates into total light output within a specific area. While both units measure light, they represent different physical concepts.

What is Candela (cd)?

Candela measures luminous intensity. It tells you how bright a light source is in one specific direction. Think of it like the pressure of water in a hose; it represents the concentration of light.

What are Lumens (lm)?

Lumens measure luminous flux. This is the total amount of visible light emitted by a source in all directions within a defined beam angle. To continue the water analogy, lumens represent the total volume of water flowing out of the hose per second.

The Mathematical Formula

To convert from candela (intensity) to lumens (total output), you must know the beam angle. The formula uses the solid angle in steradians:

Φv(lm) = Iv(cd) × 2π × [1 – cos(θ / 2)]

Where:

• Φv: Luminous flux in lumens.
• Iv: Luminous intensity in candela.
• θ: The apex angle (beam angle) in degrees.

Practical Examples

Example 1: You have a spotlight with an intensity of 1,500 candela and a narrow beam angle of 30 degrees.
Calculation: 1500 × 2π × [1 – cos(15°)] ≈ 321.4 Lumens.

Example 2: A standard LED floodlight emits 800 candela with a wide beam angle of 120 degrees.
Calculation: 800 × 2π × [1 – cos(60°)] = 800 × 2π × 0.5 ≈ 2,513.3 Lumens.

Why Beam Angle Matters

A light with high candela doesn't always mean high lumens. A laser pointer has incredibly high candela because its beam is very concentrated, but its total lumen count is very low. Conversely, a standard household light bulb has a lower candela rating but higher lumens because it spreads light in almost every direction.

function calculateLumens() { var candela = document.getElementById("candelaInput").value; var angle = document.getElementById("angleInput").value; var resultArea = document.getElementById("resultArea"); var lumenResult = document.getElementById("lumenResult"); var resultText = document.getElementById("resultText"); if (candela === "" || angle === "" || candela <= 0 || angle 360) { alert("Beam angle cannot exceed 360 degrees."); return; } // Formula: Lumens = Candela * 2 * PI * (1 – cos(AngleInRadians / 2)) var angleInRadians = (angle * Math.PI) / 180; var solidAngle = 2 * Math.PI * (1 – Math.cos(angleInRadians / 2)); var lumens = candela * solidAngle; lumenResult.innerHTML = lumens.toLocaleString(undefined, { minimumFractionDigits: 2, maximumFractionDigits: 2 }) + " lm"; resultText.innerHTML = "A light source of " + candela + " cd with a " + angle + "° beam produces " + lumens.toFixed(2) + " lumens."; resultArea.style.display = "block"; }