Lens Radius of Curvature Calculator

Enter Lens Data

Calculation method

Focal length

Focal length unit

Lens refractive index

Surrounding medium index

Known second surface radius

Second radius unit

Clear aperture diameter

Diameter unit

Sagitta or center depth

Sagitta unit

Surface power in diopters

Diopter radius sign

Formula Used

Thin lensmaker equation in a surrounding medium:

1 / f = (n_lens / n_medium - 1) × (1 / R1 - 1 / R2)

Symmetric lens: R = 2 × (n_lens / n_medium - 1) × f

Plano lens: R = (n_lens / n_medium - 1) × f

Sagitta method: R = (a² + s²) / (2s), where a is half the clear diameter.

Surface power method: R = (n2 - n1) / P, where P is surface power in diopters.

Positive and negative radius signs follow the common paraxial sign convention. For final optical production, verify signs against your design standard.

How to Use This Calculator

Select a calculation method, or keep auto mode for every possible result.
Enter focal length, refractive indices, radius, sagitta, diameter, or diopter data.
Choose the correct units for each length input.
Press the calculate button to show results above the form.
Review the graph, then export CSV or PDF for records.

Example Data Table

Case	Focal Length	Lens Index	Diameter	Sagitta	Typical Output
Small convex lens	50 mm	1.52	25 mm	1.6 mm	About 50 mm symmetric radius
Camera element	85 mm	1.60	40 mm	2.4 mm	About 102 mm symmetric radius
Lab demonstration lens	100 mm	1.52	50 mm	3.2 mm	About 104 mm symmetric radius

Understanding Lens Radius of Curvature

A lens radius of curvature describes how strongly a lens surface bends. A small radius means a tighter curve. A large radius means a flatter surface. This value matters in cameras, microscopes, telescopes, spectacles, and lab optics. It also affects focal length, optical power, aberration, and image quality.

Why Radius Matters

Optical designers use radius values to control how light refracts. A biconvex lens usually has one positive and one negative surface radius. A plano lens has one curved face and one flat face. A meniscus lens uses two curved surfaces with different signs. Correct signs help match the real direction of light travel.

Methods Used By This Tool

This calculator supports several practical routes. The lensmaker route estimates radius from focal length and refractive index. The second surface route solves the first radius when another radius is known. The sagitta route uses lens diameter and center depth. The diopter route converts surface power into radius.

Good Input Practice

Use consistent measurements. Choose the right unit before pressing calculate. Enter focal length as positive for converging lenses. Enter negative focal length for diverging lenses. Use realistic refractive index values. Crown glass is often near 1.52. Water is near 1.33. Air is close to 1.00.

Reading The Results

The summary shows radius in meters, millimeters, and centimeters. It also reports curvature, focal power, and estimated sagitta when enough data exists. Curvature is the inverse of radius. The chart helps you see how radius changes with sagitta or focal length. This is useful for checking sensitivity.

Design Notes

Thin lens formulas are excellent for early design and education. Thick lenses need extra data, such as center thickness and principal plane positions. Manufacturing tolerances also matter. Always verify final optical designs with ray tracing software or precise laboratory measurements before production.

Common Use Cases

Students use radius estimates to connect geometry with refraction. Makers use them before grinding or ordering lenses. Teachers use them for classroom experiments. Engineers use them for quick feasibility checks. The exported report is helpful for notes, worksheets, and comparison records. Keep assumptions visible when sharing results with others during review.

FAQs

1. What is lens radius of curvature?

It is the radius of the imaginary sphere matching a lens surface. A smaller radius means a stronger curve. A larger radius means a flatter surface.

2. Can this calculator handle convex and concave lenses?

Yes. Enter positive focal length for converging lenses. Enter negative focal length for diverging lenses. Use radius signs according to your optical convention.

3. What is sagitta?

Sagitta is the center depth between a curved surface and its chord. In lens work, it often means the surface rise across the clear aperture.

4. Why do refractive indices matter?

Refraction depends on index contrast. A higher lens index bends light more strongly. The same focal length may need a different radius in another medium.

5. Is this suitable for thick lenses?

It gives useful early estimates. Thick lenses need center thickness, spacing, and principal plane data. Use ray tracing for final professional optical design.

6. What does diopter power mean?

Diopter power is inverse focal length in meters. A 100 mm focal length equals 10 diopters. Surface power uses index change divided by radius.

7. Why are some radius values negative?

Negative signs describe surface direction under a chosen sign convention. They do not always mean the lens is invalid. They show curvature orientation.

8. Can I export the results?

Yes. Use the CSV button for spreadsheet work. Use the PDF button for a simple report containing inputs, results, and notes.