Calculate optical power in diopters or focal length in meters, cm, mm, inches, or feet using the thin-lens formula D = 1/f for lenses.
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Dioptric Power Formula
The calculator uses the thin-lens relationship between dioptric power and focal length in air. Dioptric power is the reciprocal of focal length measured in meters.
- D = dioptric power in diopters, also written as m-1
- f = focal length in meters
If you enter focal length, the calculator converts that length to meters and solves D = 1/f. If you enter dioptric power, it solves f = 1/D, then converts the focal length into the unit you selected.
A positive diopter value indicates a converging lens. A negative diopter value indicates a diverging lens. A zero value cannot be used because division by zero is undefined.
Common Diopter and Focal Length Values
These values can help you check whether a result is in the expected range.
| Dioptric Power | Focal Length | Lens Type |
|---|---|---|
| +10 D | 0.10 m, or 10 cm | Strong converging lens |
| +5 D | 0.20 m, or 20 cm | Converging lens |
| +2 D | 0.50 m, or 50 cm | Converging lens |
| -2 D | -0.50 m, or -50 cm | Diverging lens |
| -5 D | -0.20 m, or -20 cm | Diverging lens |
Focal Length Unit Conversions
| Unit | Meters Equivalent |
|---|---|
| 1 meter | 1 m |
| 1 centimeter | 0.01 m |
| 1 millimeter | 0.001 m |
| 1 inch | 0.0254 m |
| 1 foot | 0.3048 m |
Example Calculations
Example 1: Calculate diopters from focal length
You have a lens with a focal length of 25 cm. First convert centimeters to meters:
25 cm = 0.25 m
The dioptric power is +4 D.
Example 2: Calculate focal length from diopters
You have a lens with an optical power of -2.5 D.
The focal length is -0.4 m, or -40 cm. The negative sign means the lens is diverging.
FAQ
What is a diopter?
A diopter is a unit of optical power. It is equal to the reciprocal of focal length in meters. For example, a lens with a focal length of 0.5 m has a power of 2 D because 1 ÷ 0.5 = 2.
Why does focal length need to be in meters?
The diopter is defined as inverse meters, or m-1. If focal length is entered in centimeters, millimeters, inches, or feet, it must be converted to meters before using the formula.
What does a negative diopter value mean?
A negative diopter value means the lens is diverging. Diverging lenses have negative focal lengths under the standard sign convention. A positive value means the lens is converging.
