Projection Lens Design Calculator

Simple Symmetrical Duplet Lens Designer.

The formula used in this simple lens designer to calculate effective focal length is:

Effective Focal Length = Element one focal length * Element two focal length/((Element one focal length + Element two focal length) - the Distance between the elements)

The only trick to using this calculator is that if you enter one measurement in mm then they all have to be in mm. Likewise if you enter one measurement in inches then they all have to be in inches. This calculator works with both meniscus lenses and plano convex lenses.

Lenses designed using this calculator will have a field of view of 30 degrees.


Enter the focal length of lens 1.
Enter the focal length of lens 2.
Enter the distance between the principal planes of the two lenses.
Enter the clear diameter of the smallest lens after mounting.
Focal Length of the duplet in mm.


Use this chart for making Symmetrical Duplet lenses. The exact specifications are not particularly critical. Duplet design is very forgiving.

For example suppose you need a 9" lens. You would need lens elements that are more than 71 mm in diameter and that have a focal length of about 391.6 mm (400mm is ok). You would need to mount them in a suitable tube about 114.3 mm apart. You would also need to mount a disc of black, thin cardboard or a disc of black, sheet metal shim stock with a hole cut in the center that is about 38.4mm between the two lens elements. That is all there is to it.

You may be wondering about the f number of the lens. F numbers are calculated using this formula F number = E.F.L. / Entrance Pupil Diameter. Once you gather your parts together you can use the above calculator for a more exact focal length calculation. Lenses designed using this Chart are about F5. I suppose you give up something to be able to make the lens you need when you need it.

Symmetrical Duplets like these are used everywhere. In fact, just about every overhead projector that has been manufactured uses a simple Symmetrical Duplet lens as the "objective" or focusing lens.

lens E.F.L. lens E.F.L. element F.L. distance aperture stop
in inches in mm in mm in mm in mm in mm
1 25.4 43.4 12.7 7.9 4.3
1.5 38.1 65.0 19.1 11.7 6.4
2 50.8 86.9 25.4 15.9 8.6
2.5 63.5 108.7 31.8 19.6 10.7
3 76.2 130.4 38.1 23.5 12.8
3.5 88.9 152.2 44.5 27.5 15.0
4 101.6 174.0 50.8 31.4 17.1
4.5 114.3 195.8 57.2 35.3 19.2
5 127 217.5 63.5 39.2 21.4
5.5 139.7 239.3 69.9 43.2 23.5
6 152.4 261.0 76.2 47.1 25.6
6.5 165.1 282.8 82.6 51.0 27.8
7 177.8 304.6 88.9 54.9 29.9
7.5 190.5 326.3 95.3 58.9 32.0
8 203.2 348.1 101.6 62.8 34.2
8.5 215.9 369.9 108.0 66.7 36.3
9 228.6 391.6 114.3 70.6 38.4
9.5 241.3 413.4 120.7 74.6 40.6
10 254 435.2 127 78.5 42.7
10.5 266.7 457.0 133.4 82.4 44.8
11 279.4 478.7 139.7 86.3 46.9
11.5 292.1 500.5 146.1 90.3 49.1
12 304.8 522.2 152.4 94.2 51.2
12.5 317.5 544.0 158.8 98.1 53.4
13 330.2 565.8 165.1 102.0 55.5
13.5 342.9 587.6 171.5 106.0 57.6
14 355.6 609.3 177.8 109.9 59.8
14.5 368.3 631.1 184.2 113.8 61.9
15 381 652.9 190.5 117.7 64.0
15.5 393.7 674.6 196.9 121.6 66.2
16 406.4 696.4 203.2 125.6 68.3
16.5 419.1 718.2 209.6 129.5 70.4
17 431.8 739.9 215.9 133.4 72.6
17.5 444.5 761.7 222.3 137.3 74.7
18 457.2 783.5 228.6 141.3 76.8
18.5 469.9 805.2 235.0 145.2 79.0
19 482.6 827.0 241.3 149.1 81.1
19.5 495.3 848.8 247.7 153.0 83.2
20 508 870.5 254 157.0 85.4
20.5 520.7 892.3 260.4 160.9 87.5
21 533.4 914.1 266.7 164.8 89.6
21.5 546.1 935.8 273.1 168.7 91.8
22 558.8 957.6 279.4 172.7 93.9
22.5 571.5 979.4 285.8 176.6 96.0
23 584.2 1001.1 292.1 180.5 98.2
23.5 596.9 1022.9 298.5 184.4 100.3
24 609.6 1044.7 304.8 188.4 102.4