The formula to calculate Lumens (\(lm\)) from Candela (\(cd\)) is:
\[ lm = cd \times (2 \pi (1 - \cos(\theta / 2))) \]
Where:
Lumens (lm) measure the total amount of visible light emitted by a source. Candela (cd) measures the luminous intensity in a specific direction.
The beam angle is the angle at which the light is emitted from the source.
Let's assume the following values:
Using the formula:
\[ lm = 100 \times (2 \pi (1 - \cos(30 / 2))) \]
Evaluating:
\[ lm = 100 \times (2 \pi (1 - \cos(15))) \]
The Lumens is approximately 21.41 lm.
| Candela (cd) | Beam Angle (degrees) | Lumens (lm) |
|---|---|---|
| 10 | 10 | 0.2391 |
| 10 | 20 | 0.9546 |
| 10 | 30 | 2.1409 |
| 10 | 40 | 3.7892 |
| 10 | 50 | 5.8869 |
| 10 | 60 | 8.4179 |
| 10 | 70 | 11.3630 |
| 10 | 80 | 14.6999 |
| 10 | 90 | 18.4030 |
| 20 | 10 | 0.4782 |
| 20 | 20 | 1.9091 |
| 20 | 30 | 4.2819 |
| 20 | 40 | 7.5784 |
| 20 | 50 | 11.7737 |
| 20 | 60 | 16.8357 |
| 20 | 70 | 22.7260 |
| 20 | 80 | 29.3997 |
| 20 | 90 | 36.8060 |
| 30 | 10 | 0.7173 |
| 30 | 20 | 2.8637 |
| 30 | 30 | 6.4228 |
| 30 | 40 | 11.3677 |
| 30 | 50 | 17.6606 |
| 30 | 60 | 25.2536 |
| 30 | 70 | 34.0890 |
| 30 | 80 | 44.0996 |
| 30 | 90 | 55.2091 |
| 40 | 10 | 0.9564 |
| 40 | 20 | 3.8182 |
| 40 | 30 | 8.5638 |
| 40 | 40 | 15.1569 |
| 40 | 50 | 23.5474 |
| 40 | 60 | 33.6715 |
| 40 | 70 | 45.4520 |
| 40 | 80 | 58.7994 |
| 40 | 90 | 73.6121 |
| 50 | 10 | 1.1955 |
| 50 | 20 | 4.7728 |
| 50 | 30 | 10.7047 |
| 50 | 40 | 18.9461 |
| 50 | 50 | 29.4343 |
| 50 | 60 | 42.0894 |
| 50 | 70 | 56.8151 |
| 50 | 80 | 73.4993 |
| 50 | 90 | 92.0151 |
| 60 | 10 | 1.4346 |
| 60 | 20 | 5.7273 |
| 60 | 30 | 12.8457 |
| 60 | 40 | 22.7353 |
| 60 | 50 | 35.3211 |
| 60 | 60 | 50.5072 |
| 60 | 70 | 68.1781 |
| 60 | 80 | 88.1992 |
| 60 | 90 | 110.4181 |
| 70 | 10 | 1.6737 |
| 70 | 20 | 6.6819 |
| 70 | 30 | 14.9866 |
| 70 | 40 | 26.5246 |
| 70 | 50 | 41.2080 |
| 70 | 60 | 58.9251 |
| 70 | 70 | 79.5411 |
| 70 | 80 | 102.8990 |
| 70 | 90 | 128.8212 |
| 80 | 10 | 1.9128 |
| 80 | 20 | 7.6365 |
| 80 | 30 | 17.1275 |
| 80 | 40 | 30.3138 |
| 80 | 50 | 47.0948 |
| 80 | 60 | 67.3430 |
| 80 | 70 | 90.9041 |
| 80 | 80 | 117.5989 |
| 80 | 90 | 147.2242 |
| 90 | 10 | 2.1518 |
| 90 | 20 | 8.5910 |
| 90 | 30 | 19.2685 |
| 90 | 40 | 34.1030 |
| 90 | 50 | 52.9817 |
| 90 | 60 | 75.7608 |
| 90 | 70 | 102.2671 |
| 90 | 80 | 132.2988 |
| 90 | 90 | 165.6272 |
| 100 | 10 | 2.3909 |
| 100 | 20 | 9.5456 |
| 100 | 30 | 21.4094 |
| 100 | 40 | 37.8922 |
| 100 | 50 | 58.8686 |
| 100 | 60 | 84.1787 |
| 100 | 70 | 113.6301 |
| 100 | 80 | 146.9986 |
| 100 | 90 | 184.0302 |