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The formula to calculate Lumens (lm) is:
\[ \Phi_v (\text{lm}) = I_v (\text{cd}) \times (2\pi (1 - \cos(\theta / 2))) \]
Where:
Candela (cd) is a unit of luminous intensity, representing the power emitted by a light source in a particular direction. Lumen (lm) is a unit of luminous flux, representing the total amount of light emitted by a source. The conversion from candela to lumens depends on the angle over which the light is emitted.
Let's assume the following values:
Using the formula:
\[ \Phi_v = 100 \times (2\pi (1 - \cos(30 / 2))) \]
\[ \Phi_v = 100 \times (2\pi (1 - \cos(15))) \]
\[ \Phi_v = 100 \times (2\pi (1 - 0.9659)) \]
\[ \Phi_v = 100 \times (2\pi \times 0.0341) \]
\[ \Phi_v = 100 \times 0.214 \]
The Lumens (lm) is approximately 21.4 lm.
| Candela (cd) | Lumens (lm) | Angle (degrees) |
|---|---|---|
| 1000 | 841.787 | 60 |
| 2000 | 1,683.574 | 60 |
| 3000 | 2,525.362 | 60 |
| 4000 | 3,367.149 | 60 |
| 5000 | 4,208.936 | 60 |
| 6000 | 5,050.723 | 60 |
| 7000 | 5,892.511 | 60 |
| 8000 | 6,734.298 | 60 |
| 9000 | 7,576.085 | 60 |
| 10000 | 8,417.872 | 60 |
| 11000 | 9,259.659 | 60 |
| 12000 | 10,101.447 | 60 |
| 13000 | 10,943.234 | 60 |
| 14000 | 11,785.021 | 60 |
| 15000 | 12,626.808 | 60 |
| 16000 | 13,468.595 | 60 |
| 17000 | 14,310.383 | 60 |
| 18000 | 15,152.170 | 60 |
| 19000 | 15,993.957 | 60 |
| 20000 | 16,835.744 | 60 |
| 21000 | 17,677.532 | 60 |
| 22000 | 18,519.319 | 60 |
| 23000 | 19,361.106 | 60 |
| 24000 | 20,202.893 | 60 |
| 25000 | 21,044.680 | 60 |
| 26000 | 21,886.468 | 60 |
| 27000 | 22,728.255 | 60 |
| 28000 | 23,570.042 | 60 |
| 29000 | 24,411.829 | 60 |
| 30000 | 25,253.616 | 60 |
| 31000 | 26,095.404 | 60 |
| 32000 | 26,937.191 | 60 |
| 33000 | 27,778.978 | 60 |
| 34000 | 28,620.765 | 60 |
| 35000 | 29,462.553 | 60 |
| 36000 | 30,304.340 | 60 |
| 37000 | 31,146.127 | 60 |
| 38000 | 31,987.914 | 60 |
| 39000 | 32,829.701 | 60 |
| 40000 | 33,671.489 | 60 |
| 41000 | 34,513.276 | 60 |
| 42000 | 35,355.063 | 60 |
| 43000 | 36,196.850 | 60 |
| 44000 | 37,038.637 | 60 |
| 45000 | 37,880.425 | 60 |
| 46000 | 38,722.212 | 60 |
| 47000 | 39,563.999 | 60 |
| 48000 | 40,405.786 | 60 |
| 49000 | 41,247.574 | 60 |
| 50000 | 42,089.361 | 60 |
| 51000 | 42,931.148 | 60 |
| 52000 | 43,772.935 | 60 |
| 53000 | 44,614.722 | 60 |
| 54000 | 45,456.510 | 60 |
| 55000 | 46,298.297 | 60 |
| 56000 | 47,140.084 | 60 |
| 57000 | 47,981.871 | 60 |
| 58000 | 48,823.658 | 60 |
| 59000 | 49,665.446 | 60 |
| 60000 | 50,507.233 | 60 |