How to read a polar diagram
One picture shows where a luminaire sends its light, and how much.
What a polar diagram is
A luminaire is a complete light fitting. A polar diagram shows its luminous intensity in each direction.
Luminous intensity is the strength of the light in one direction. Its unit is the candela (cd). This page calls it intensity.
Think of a vertical slice through the luminaire. The diagram draws the intensity around that slice.
Each slice holds two C-planes, for example C0 and C180. A C-plane is a vertical half-plane that starts at the axis of the luminaire. Its name is its horizontal angle C.
The example is a round downlight. Its light is the same in every C-plane, so one curve is enough.
How to read it
The numbers on the diagram match the notes beside it.
- The luminaire is at the centre. Every direction starts there.
- The gamma angle runs around the diagram. 0° points straight down. 90° is horizontal. 180° points straight up.
- Each ring is one intensity value. The ring shows its value.
- The unit is cd/klm: candela for each 1000 lumens of lamp flux. The lumen (lm) is the unit of the total light. Some diagrams use cd, which is the absolute value.
- The curve shows the intensity in one pair of C-planes. A point far from the centre means a high intensity in that direction.
- The peak is the point farthest from the centre. For this downlight the peak is straight down.
A luminaire that is not round
The second example is a linear pendant. It sends light down and up, and its light differs between C-planes.
The diagram draws two curves. C0–C180 is the slice across the pendant. C90–C270 is the slice along it.
The curve across the pendant is narrow. The curve along the pendant is wide.
The upper half of the diagram shows the light that goes up to the ceiling. A downlight has no upper half.
What numbers you can take from it
The beam angle
The beam angle is the full angle between the two directions where the intensity is 50% of the peak.
- Read the peak. For the downlight it is 1926 cd/klm.
- Take half of it: 963 cd/klm.
- Find where the curve crosses that value on each side. It crosses at 20° on the left and at 20° on the right.
- Add the two angles. The beam angle is 40°.
The pendant has two beam angles: 65.6° across it and 101.9° along it.
From cd/klm to candela
Multiply the cd/klm value by the lamp flux in lumens, then divide by 1000.
A version of the downlight that emits 1500 lumens has a peak of 1926 × 1500 ÷ 1000 = 2889 cd.
This is why vendors use cd/klm. One diagram serves every lumen version of the same luminaire design.
Where it comes from in the file
The diagram draws numbers that the photometric file already holds. The diagram adds nothing.
| Part of the diagram | IES file | LDT file |
|---|---|---|
| The angles around the diagram | Vertical angles | Gamma angles |
| Which slices exist | Horizontal angles | C-plane angles and the symmetry indicator |
| The curve | Candela values, times the candela multiplier and the ballast factor | Intensity values, already in cd/klm |
| The step between cd and cd/klm | Lumens per lamp, times the number of lamps | Total luminous flux |
The curve goes through the measured points only. A file with 5° steps gives a curve with a corner every 5°.
Why two vendors' diagrams differ
Two diagrams of the same luminaire can look different. The light is the same. The drawing choices differ.
- Unit. One diagram uses cd, the other cd/klm. The shapes match, but the ring values do not.
- Ring scale. The outer ring can be 300 or 1000. The same curve then fills the diagram or sits small in the centre.
- Planes. One vendor draws C0–C180 only. Another adds C90–C270, or a plane at 45°.
- Half or full circle. A diagram of the lower half hides any light that goes up.
- Absolute photometry. Many LED files give no lamp lumens. The program then uses the luminaire flux for cd/klm.
- Peak or centre. The CIE definition of the beam angle uses the intensity at the centre of the beam. Many programs use the peak. The results differ when the peak is off centre.
- Smoothing. Some programs round the corners of the curve. The measured points stay the same.
Same diagram, four styles
The data is the same in all four. Only the style changes. Read about diagram styles.
Sources
- CIE e-ILV 17-25-091, distribution curve of luminous intensity. The definition of the curve, normally drawn in polar coordinates.
- CIE e-ILV 17-25-090, (C, γ) coordinate system. The C-planes and the gamma angle.
- CIE e-ILV 17-21-045, luminous intensity. The definition of luminous intensity and of the candela as lumen per steradian.
- CIE e-ILV 17-27-077, beam angle. The 50% rule, and that the beam angle is a full angle.
- BIPM, SI base unit: candela. The candela as the SI unit of luminous intensity.
- CIE 121:1996, The Photometry and Goniophotometry of Luminaires. The measurement method behind the numbers.
- EN 13032-2:2017, Presentation of data for indoor and outdoor work places. The European standard for the presentation of photometric data. Catalogue page.
- ANSI/IES LM-63-19, reaffirmed 2025. The angle lists, the candela values, and absolute photometry in the IES file. Catalogue page.
- DIALux evo, Description of the EULUMDAT format. The angle lists and the cd/klm values in the LDT file.