Diopter Calculator

Convert between lens power (diopters) and focal length with correct plus and minus sign handling, and optionally combine two lens powers or estimate simple magnifier power.

What do you want to calculate?

Pick the task. This hides inputs that are not needed so you do not mix formulas.

Focal length (selected unit)

Distance from the lens to the focus for parallel light. Use a negative value for a diverging lens if you are using the sign convention (example: -0.50 m). Required in conversion modes that start from focal length.

Focal length unit

Choose the unit for focal length. The calculator converts internally to meters (m) before doing the math.

Lens power (diopters, D)

Optical power in diopters (1/m). Positive is converging (plus lens). Negative is diverging (minus lens). Required in conversion modes that start from diopters.

Second lens power to combine (diopters, D)

Use this only in the “Combine two lenses” mode. For thin lenses close together in air, powers add: total diopters = D1 + D2.

Advanced options

Combining lenses

Combine method

Use “add diopters” when lenses are thin and very close together. If lenses are separated or thick, this simple method may be inaccurate.

Magnifier estimate (optional)

Show simple magnifier estimate?

Optional. Estimates magnifying power using an assumed near point. This is a rough optics estimate, not an eyeglass prescription tool.

Near point assumption (mm)

The assumed closest comfortable viewing distance for the eye used in simple magnifier math. Commonly set to 250 mm in many optics references. Only used if magnifier estimate is turned on.

Calculating…

Lens type from sign

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Converging (plus) lenses have positive diopters. Diverging (minus) lenses have negative diopters. 0 D is no optical power.

Optical power (diopters, D)

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Bigger absolute value means a stronger lens. Example: +4 D is stronger than +2 D.

Focal length (meters)

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A positive focal length goes with a converging lens. A negative focal length goes with a diverging lens.

Focal length (millimeters)

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Useful for small focal lengths like camera or magnifier lenses.

Combined power (diopters, D)

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If the combined power is 0 D, the combination acts like no lens (in this simplified model).

Combined focal length (meters)

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If D_total is 0, the combined focal length is not defined (it would be infinite).

Estimated magnifying power (times)

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This estimate depends on the near point assumption and viewing method. Do not use it to self-prescribe eyewear.

Notes and warnings

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If you see “N/A”, change the input to avoid dividing by zero.

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How to use our Diopter Calculator

Choose a task in "What do you want to calculate?" (this hides inputs you do not need).
If you chose a focal-length-based task, pick the "Focal length unit" and enter "Focal length (selected unit)" (use a negative value if you are using the diverging-lens sign convention).
If you chose a diopter-based task, enter "Lens power (diopters, D)" (positive for a converging/plus lens, negative for a diverging/minus lens).
If you chose "Combine two lenses", enter the first lens power in "Lens power (diopters, D)" and the second in "Second lens power to combine (diopters, D)".
Open "Advanced options" only if you need them.
In Advanced options, set "Combine method" (the default assumes thin lenses very close together, where powers add).
To see the magnifier estimate, set "Show simple magnifier estimate?" to Yes, then set "Near point assumption (mm)" (250 mm is a common default).
Click "Calculate" and read the output cards. If you see "N/A", adjust the input to avoid dividing by zero.

Definitions

Diopter (D): Lens "strength". It is optical power measured in 1 per meter (1/m). A bigger absolute value means a stronger lens. [2]

Focal length: The distance where parallel light rays come to a focus (or appear to come from) for a lens. [4]

Converging (plus) lens: A lens with positive diopters and positive focal length in the common sign convention.

Diverging (minus) lens: A lens with negative diopters and negative focal length in the common sign convention.

Thin lenses close together: A common approximation where you can add lens powers (diopters) if lenses are thin and very near each other. [1]

Near point (assumption): An assumed closest comfortable viewing distance used in simple magnifier estimates (often 250 mm). [3]

Methodology

What the calculator is doing

All conversions are based on the standard optics idea that diopters are the reciprocal of focal length in meters, keeping the sign. [2]

Step 1: Convert the entered focal length to meters (when needed)

f_m = f_selected * factor_to_m

Conversion factors used:

m to m = 1, cm to m = 0.01, mm to m = 0.001. (These are exact unit conversions.) [3]

f_mm = f_m * 1000

Mode A: Diopters from focal length

D = 1 / f_m

If focal length equals 0, the calculator blocks the calculation with an error because division by zero is not allowed. Negative focal length produces negative diopters (diverging lens) and positive focal length produces positive diopters (converging lens). [4]

Mode B: Focal length from diopters

f_m = 1 / D

If diopters equals 0, focal length would be infinite (no focusing power). The calculator shows focal length as N/A, but it still reports lens type as "0 D (no optical power)". [2]

Mode C: Combine two lenses (thin, close together)

D_total = D1 + D2

f_total_m = 1 / D_total

If the combined power equals 0 D, the combined focal length is not defined (it would be infinite), so the calculator shows N/A for combined focal length but still shows D_total = 0. This simple adding rule is a thin-lens, close-together approximation. [1]

Optional: Simple magnifier estimate (only when enabled)

MP = near_point_mm / f_mm

This is an estimate that depends on the near point assumption (default 250 mm). Small focal lengths (or very large diopters) can make MP change a lot with tiny input changes, so the calculator may show a note when values are extreme. [3]