Diopter Conversion
A lens of 2 diopters has a focal length of 500 millimetres, which is half a metre.
Quick answer: Divide 1,000 by the power in diopters to get millimetres. For example, 2 diopters is 500 mm, 1 diopters is 1,000 mm and 4 diopters is 250 mm.
The diopter conversion formula
Focal length in metres equals one divided by the power in diopters.
Multiply by 1,000 for millimetres or by 100 for centimetres.
Take 2 diopters. 1,000 ÷ 2 gives 500 mm.
Take 1 diopters. 1,000 ÷ 1 gives 1,000 mm.
Power is the inverse of focal length
A diopter is the reciprocal of focal length in metres, so a stronger lens has a shorter focal length (Warby Parker: What Is a Diopter).
A 1 diopter lens focuses at 1 metre, a 2 diopter lens at half a metre and a 3 diopter lens at one third of a metre.
How to convert diopter conversion step by step
- Read the lens power in diopters.
- Divide 1,000 by the power for millimetres.
- Divide 100 by the power for centimetres.
- Use a positive value for a converging lens.
Example 1: 2 diopters
- Start with 2 diopters.
- 1,000 ÷ 2 = 500.
- The focal length is 500 mm.
2 diopters = 500 mm
Example 2: 1 diopters
- Start with 1 diopters.
- 1,000 ÷ 1 = 1,000.
- The focal length is 1,000 mm.
1 diopters = 1,000 mm
Example 3: 4 diopters
- Start with 4 diopters.
- 1,000 ÷ 4 = 250.
- The focal length is 250 mm.
4 diopters = 250 mm
The three examples below use common sizes.
Each one shows the sum in full.
diopter conversion conversion table
| Lens power | Focal length (mm) | Focal length (cm) |
|---|---|---|
| 0.25 diopters | 4,000 mm | 400 cm |
| 0.5 diopters | 2,000 mm | 200 cm |
| 0.75 diopters | 1,333.33 mm | 133.33 cm |
| 1 diopters | 1,000 mm | 100 cm |
| 1.5 diopters | 666.67 mm | 66.667 cm |
| 2 diopters | 500 mm | 50 cm |
| 2.5 diopters | 400 mm | 40 cm |
| 3 diopters | 333.33 mm | 33.333 cm |
| 4 diopters | 250 mm | 25 cm |
| 5 diopters | 200 mm | 20 cm |
| 10 diopters | 100 mm | 10 cm |
| 20 diopters | 50 mm | 5 cm |
The highlighted row is the default of the calculator. The last column gives cm.
A quick mental shortcut for diopter conversion
Divide 100 by the diopters to get centimetres. A 4 diopter lens has a focal length of 25 centimetres.
Double the power and the focal length halves.
Reading glasses
Reading glasses usually carry a positive value, which is added to your distance prescription (Warby Parker: What Is a Diopter).
A +2.00 lens focuses at 50 centimetres, a comfortable reading distance for many people.
Stronger means shorter
A lens with more diopters bends light more, so its focal point is closer. A 10 diopter lens focuses at only 10 centimetres.
This is why magnifiers use high powers.
Plus and minus
Positive powers use convex lenses for farsightedness. Negative powers use concave lenses for nearsightedness (Warby Parker: What Is a Diopter).
This page gives the size of the focal length and ignores the sign.
Quick conversion answers
| Conversion | Result |
|---|---|
| 1 diopters | 1,000 mm |
| 2 diopters | 500 mm |
| 4 diopters | 250 mm |
| 10 diopters | 100 mm |
Where this conversion is used
Students link lens power and focal length.
Hobbyists pick close-up lenses for cameras.
Common mistakes to avoid
- Multiplying instead of dividing. The focal length is the inverse.
- Using centimetres in the formula. Diopters use metres.
- Ignoring the sign. Negative lenses spread light out.
- Treating a prescription as a focus distance. It is a lens power.
Related converters
More lens powers
0.125 diopters is 8,000 mm. 0.375 diopters is 2,667 mm. 1.25 diopters is 800 mm.
1.75 diopters is 571.4 mm. 2.25 diopters is 444.4 mm. 3.5 diopters is 285.7 mm.
6 diopters is 166.7 mm. 8 diopters is 125 mm. 15 diopters is 66.67 mm.
Doubling the first number
0.25 diopters is 4,000 mm. 0.75 diopters is 1,333 mm. 2.5 diopters is 400 mm.
3.5 diopters is 285.7 mm. 4.5 diopters is 222.2 mm. 7 diopters is 142.9 mm.
12 diopters is 83.33 mm. 16 diopters is 62.5 mm. 30 diopters is 33.33 mm.
Common lens powers
0.5 diopters is 2,000 mm. 1 diopters is 1,000 mm. 2 diopters is 500 mm.
4 diopters is 250 mm.
A full worked example
Take a lens of 2.5 diopters. Divide 1,000 by 2.5 to get 400 millimetres.
That is 40 centimetres, or 0.4 metres.
Going the other way
To find the power from a focal length, divide 1,000 by the length in millimetres. A focal length of 250 millimetres is 4 diopters.
A focal length of 2,000 millimetres is 0.5 diopters.
Doubling and halving
Double the power and the focal length halves. 1 diopter is 1,000 millimetres and 2 diopters is 500 millimetres.
Halve the power and the focal length doubles. 0.5 diopters is 2,000 millimetres.
Checking the answer
Divide 1,000 by your answer in millimetres. You should get the diopters you started with.
For 400 millimetres, 1,000 divided by 400 gives 2.5 again.
Rounding the answer
Focal lengths are usually given to the nearest millimetre. A power of 3.5 diopters gives 285.7 millimetres, which is 286 millimetres.
Round only at the end, so small errors do not build up.
Everyday powers in millimetres
A lens of 0.25 diopters has a focal length of 4,000 millimetres. A lens of 0.5 diopters has 2,000 millimetres, and 0.75 diopters has about 1,333 millimetres.
A lens of 1.5 diopters has about 667 millimetres, and 3 diopters has about 333 millimetres.
Why the sign does not change the length
A plus lens and a minus lens of the same size have focal lengths of the same size, but one gathers light and the other spreads it.
So a power of minus 2 diopters still gives a length of 500 millimetres in size.
Using the table
Find your power in the quick table and read across to the focal length. If your power is between two rows, use the formula for the exact value.
The highlighted row is the default of the calculator.
Frequently asked questions
How do I convert diopters to focal length?
Divide 1 by the diopters to get metres, or 1,000 by the diopters to get millimetres.
What is the focal length of a 2 diopter lens?
500 millimetres, or 50 centimetres.
What does a higher diopter mean?
A stronger lens with a shorter focal length.
What is a 1 diopter lens?
A lens that focuses at 1 metre.
Do reading glasses use plus values?
Yes, usually positive powers.
Can I convert millimetres back to diopters?
Divide 1,000 by the focal length in millimetres.
Sources
- Warby Parker: What Is a Diopter (warbyparker.com)
