Y2calculate

Candela to Lumens Calculator

What is Candela and Lumens?

Candela (cd)

  • Definition: Candela is the SI unit of luminous intensity. It measures the amount of light emitted by a source in a particular direction.
  • Meaning: Think of candela as the “brightness” of a light source when viewed from a specific direction. For example, a laser beam, which focuses light in one direction, has a high candela value.
  • Practical Example: A common candle emits light with an intensity of roughly 1 candela. This is where the unit gets its name.

Lumens (lm)

  • Definition: Lumens measure the total amount of visible light emitted by a source in all directions. It is the SI unit for luminous flux.
  • Meaning: Lumens describe how much light a source produces overall, regardless of the direction. A higher lumen value means a brighter light overall.
  • Practical Example: A standard 60-watt incandescent bulb produces around 800 lumens.

Candela to Lumens Conversion

Formula: Candela to Lumens

The luminous flux (\( \Phi_v \)) in lumens is calculated as:

\[ \Phi_v (\text{Lumens}) = I_v (\text{Candela}) \times \Omega (\text{Steradians}) \]

Where:

  • \( \Phi_v \) = Luminous flux in lumens
  • \( I_v \) = Luminous intensity in candela
  • \( \Omega \) = Solid angle in steradians

Formula: Solid Angle (\( \Omega \))

The solid angle is calculated as:

\[ \Omega (\text{Steradians}) = 2 \pi \times (1 - \cos(\frac{\theta}{2})) \]

Where:

  • \( \theta \) = Cone apex angle in degrees

Combined Formula

Combining the two formulas:

\[ \Phi_v (\text{Lumens}) = I_v (\text{Candela}) \times [2 \pi \times (1 - \cos(\frac{\theta}{2}))] \]

Example Calculation

If the luminous intensity is 10 candela and the cone apex angle is 60 degrees:

\[ \Omega = 2 \pi \times (1 - \cos(60^\circ / 2)) = 2 \pi \times (1 - \cos(30^\circ)) \]

\[ \Phi_v = 10 \times \Omega = 10 \times [2 \pi \times (1 - \cos(30^\circ))] \]

Difference Between Candela and Lumens

AspectCandelaLumens
What it MeasuresLuminous intensity (brightness in a specific direction)Total light output (overall brightness)
DirectionDirectional (focused light)Omnidirectional (all light emitted)
ExampleA flashlight with a narrow beamA light bulb lighting a whole room

Relationship Between Candela and Lumens

The connection depends on the geometry of the light source. Specifically:

Lumens=Candela×Solid Angle (steradians)

A light source with a high candela value but a narrow beam might produce fewer lumens than a source with a lower candela value but a wider beam.

Analogy

  • Candela: How bright the light seems from a specific angle (like the beam of a flashlight).
  • Lumens: How much light the source spreads out in total (like the brightness of a light bulb in a room).

Candela to Lumen conversion Table

QuestionAnswer
100,000 candela to lumens628,318.53 lumens
66,000 candela to lumens414,498.88 lumens
1 million candela to lumens6,283,185.31 lumens
1000 candela to lumens6,283.19 lumens
1600 candela to lumens10,053.07 lumens
3000 candela to lumens18,876.62 lumens
544,000 candela to lumens3,418,706.94 lumens
42.3 billion candela to lumens265,330,313,655.88 lumens
Candela to lumens conversionDependent on values of candela and angle
300 candela to lumens1,884.99 lumens
7 million candela to lumens43,964,203.06 lumens
10,000 candela to lumens62,831.85 lumens
230 candela to lumens1,444.80 lumens
18,000 candela to lumens113,588.07 lumens
Candela to lumens formulaΦv = Iv × (2Ï€(1 – cos(θ/2)))

How to use Candela to Lumen calculator

How to Use the Candela to Lumen Calculator:
– Step 1: Enter the luminous intensity in candela (cd).
– Step 2: Enter the cone apex angle in degrees (°).
– Step 3: The calculator computes the solid angle using:
Ω = 2Ï€ × (1 – cos(θ / 2))
– Step 4: It calculates the luminous flux (lumens) using:
Φv = Iv × Ω
– Step 5: View the result, showing the luminous flux in lumens (lm).

Example:
– Enter 10 cd for luminous intensity.
– Enter 60° for the apex angle.
– The result will show luminous flux as 7.54 lumens.

Scroll to Top