Lens Power Calculator

Lens power in diopters is the reciprocal of focal length in meters. Convex (converging) lenses have positive power; concave (diverging) have negative. Lens powers add directly in combination.

🔍 Optics📐 P = 1/f👓 Optometry
Focal Length f (cm)
Or lens power P (D)

Enter focal length OR power

Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
PowerPP = 1/f (f in meters)D (diopters)
Focal Lengthff = 1/Pm
Combined PowerPtotalP1 + P2 + P3D
1 Diopter1 DFocus at exactly 1 mm

Step-by-Step Examples

Example 1
Reading Glasses

+2 diopter lens. Find focal length.

  • f = 1/P = 1/2.0 = 0.5 m = 50 cm
✓ 50 cm focal length reading glasses
Example 2
Myopia Correction

-3.5 diopter corrective lens.

  • f = 1/(-3.5) = -0.286 m = -28.6 cm
  • Diverging lens, virtual focus
✓ Diverging lens for nearsightedness correction
Example 3
Contact Lens Combo

Eye needs -2.0 D correction. Contact on eye adds -1.5 D. Need extra power?

  • P_total = P1 + P2
  • -2.0 = -1.5 + P_extra
  • P_extra = -0.5 D
✓ Additional -0.5 D lens needed

Real-World Applications

👓
Glasses Prescriptions
Optometrist prescriptions in diopters: positive for farsightedness, negative for nearsightedness.
📷
Camera Lenses
Camera lens power determines magnification and focusing distance for photography.
🔬
Microscopes
Objective and eyepiece powers combine to give total microscope magnification.
👁️
Laser Beam Control
Lens combinations shape and focus laser beams in optical instruments.

Common Mistakes to Avoid

⚠️
Focal length must be in meters for diopters

1 D = 1/1m. If focal length is 25 cm, P = 1/0.25 = 4.0 D. Using cm without converting gives 100x error.

⚠️
Positive vs negative lens

Converging (convex) lens: positive focal length, positive power. Diverging (concave): negative focal length, negative diopters.

⚠️
Powers add only in contact

P_total = P1 + P2 works only for thin lenses in contact. Separated lenses need more complex formula.

Frequently Asked Questions

What does 1 diopter mean? ▾
A +1 D lens focuses parallel rays to a point 1 meter away. A +4 D lens focuses them at 25 cm. Stronger lens = shorter focal length.
What is a normal human eye power? ▾
The eye total power is about +60 D, with the cornea (~+43 D) and lens (~+17 D). The lens adjusts for focusing near and far.
What does -2.5 diopters in a prescription mean? ▾
Myopic (nearsighted) eye focuses 1/2.5 = 40 cm away. The corrective lens diverges light to effectively move the object to infinity.
How do progressive lenses work? ▾
Gradual change in curvature across lens provides different power zones: distance (top), intermediate, and reading (bottom) — all in one lens.
Can you add lens powers? ▾
Yes, for thin lenses in contact: P_total = P1 + P2 + P3. This is why it is easy to design compound optical systems.

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