Convert luminous intensity in candela (cd) to luminous flux in lumens (lm), using beam angle.
Formula:
Lumens = 2 × π × Candela × (1 − cos(θ / 2))Light measurement plays a vital role in lighting design, photography, cinematography, architecture, and physics. When working with directional light sources such as spotlights or flashlights, professionals often need to convert candela (cd) – a unit of luminous intensity – into lumens (lm), which represent the total luminous flux. Our Candela to Lumens Calculator makes this conversion easy, accurate, and instant, helping you make informed lighting decisions.
Candela is the SI unit of luminous intensity. It measures how much light a source emits in a particular direction. If you imagine a laser pointer or flashlight beam, candela defines how intense that beam is in one direction. One candela is roughly the light intensity of a common candle.
Lumen is the unit of luminous flux, which measures the total amount of visible light emitted by a source in all directions. Unlike candela, which is directional, lumen is about total output. More lumens mean a brighter light overall, regardless of direction.
Think of candela as a laser pointer and lumens as a light bulb. The laser pointer has a high candela but low lumens, while a light bulb emits high lumens over a wide area but lower candela in any one direction.
The formula to convert candela to lumens depends on the beam angle or solid angle of the light beam:
lumens = candela × solid angle (in steradians)In a directional beam, the light spreads out in a cone. You must calculate the solid angle in steradians from the beam angle in degrees.
For a conical beam:
Ω (steradians) = 2π × (1 - cos(θ / 2))Where θ is the full beam angle in degrees.
lumens = candela × 2π × (1 - cos(beam_angle / 2))Input: 200 cd, 30° beam angle
Solid angle: Ω = 2π × (1 - cos(15°)) ≈ 0.214 steradians
Lumens: 200 × 0.214 = 42.8 lumens
Input: 500 cd, 60° beam angle
Solid angle: ≈ 0.84 steradians
Lumens: 500 × 0.84 = 420 lumens
Lighting manufacturers often list values in candela, lumens, or both. If you’re designing a lighting setup, understanding how these values relate helps you:
| Candela (cd) | Beam Angle (°) | Approx. Lumens (lm) |
|---|---|---|
| 100 | 10° | 7.5 |
| 100 | 30° | 21 |
| 100 | 60° | 84 |
| 500 | 45° | 134 |
| 1000 | 90° | 840 |
This conversion assumes uniform light distribution across the beam, which may not be accurate for all light types. Reflectors, lenses, and beam hotspots can skew real-world results. For precise photometry, refer to IES files or manufacturer data.
No. You need the beam angle (or solid angle in steradians) to convert accurately.
It depends on the beam angle. For example, with a 90° beam, 1 candela ≈ 8.4 lumens.
A wider beam angle gives more lumens for the same candela value since light is spread out more.
Anywhere from 500 cd (floodlight) to 100,000+ cd (tactical spotlight).
Yes. Lumens indicate how bright the light appears overall. More lumens = brighter light.
The Candela to Lumens Calculator is an essential tool for lighting engineers, electricians, photographers, and anyone working with directional light sources. By understanding the relationship between beam angle and luminous intensity, you can make accurate and professional lighting decisions. Use this free tool to save time, improve accuracy, and optimize lighting design for any scenario.
Bookmark this page and share it with colleagues or clients working in lighting design, film production, architecture, or home improvement. Simplify your lighting calculations with Easy Converters!
To truly understand how candela translates into lumens, we need to dive deeper into the geometry of light. In three-dimensional space, light doesn't just move in straight lines—it spreads out in angles, forming cones. This is where the concept of the steradian becomes important.
A steradian (sr) is the SI unit of a solid angle, much like how radians are used in two dimensions. A full sphere contains exactly 4π steradians. So if you had a perfectly spherical light source emitting equally in all directions with 1 candela of intensity, its total light output would be:
lumens = candela × 4π ≈ candela × 12.57This only applies to omnidirectional sources. Most modern LED fixtures, flashlights, and architectural lights have directional beams, so we use smaller portions of the 4π solid angle.
Beam angle dramatically affects the number of lumens produced from a candela value. A tighter beam angle focuses light into a smaller area, increasing intensity but reducing overall luminous flux. Conversely, a wide beam spreads light more diffusely, reducing intensity but increasing coverage and total lumens.
Here’s a basic breakdown:
The beam angle is essential to compute lumens accurately from candela. Without it, the conversion lacks precision.
When designing lighting for commercial or residential spaces, both candela and lumens help determine proper fixture placement and selection. Here’s how:
Interior designers often work closely with electrical engineers to balance visual comfort and functional light. For example, track lights with 3000 cd intensity at a 30° beam angle provide ~630 lumens, perfect for spotlighting a feature wall.
Understanding candela-to-lumen conversions also plays a role in energy efficiency. Lumen per watt (lm/W) is a measure of lighting efficacy. Knowing how lumens relate to candela allows you to calculate how efficiently a light directs energy:
Efficiency (lm/W) = Total lumens / Power consumption (W)Modern LED lights boast high efficacy, often 100–150 lm/W, far surpassing old incandescent bulbs (10–15 lm/W). Proper beam control using candelas ensures light goes only where needed, minimizing wastage and improving system performance.
While manual formulas are great for learning, using a digital Candela to Lumens Calculator is much faster and more reliable. Our online calculator lets you:
Whether you're working on a lighting retrofit or building a new layout from scratch, having a tool like this saves time and ensures accuracy.
For advanced lighting setups, professionals use photometric diagrams and IES files (Illuminating Engineering Society format). These include:
If you have a photometry file from a manufacturer, you can find candela values at various angles and then calculate lumens for each zone using the formula above. Some software even visualizes this in 3D, allowing for simulation of room illumination and shadows.
You can embed or bookmark this tool on your design dashboards, or use it while preparing specifications for clients, especially when selecting directional lights, theatrical fixtures, stadium lighting, or spotlights. Export results to CSV or PDF (coming soon) for easier documentation and proposal sharing.
The Candela to Lumens Calculator is more than just a conversion tool—it’s a decision-making assistant. With the right numbers, you can ensure that light placement is efficient, aesthetically pleasing, and energy-conscious. Whether you're lighting a product showcase, designing a landscape layout, or setting up a home theater, using this calculator puts you in control of the science behind illumination.
Try it now and get your lighting specs right the first time!