Advanced Astigmatism Calculator

Astigmatism Calculator Form

Record label

Useful for exports and saved analysis names.

Input mode

Choose radius inputs or direct power inputs.

Meridian A axis (°)

Meridian B is automatically set 90° away.

Meridian A radius (mm)

Common corneal radius values are around 7 to 8 mm.

Meridian B radius (mm)

The smaller radius usually creates steeper power.

Keratometric refractive index

Default 1.3375 for keratometric conversion.

Meridian A power (D)

Direct dioptric power for the first meridian.

Meridian B power (D)

Direct dioptric power for the orthogonal meridian.

Sphere (optional Rx block)

Enter prescription details to compute spherical equivalent and transposition.

Cylinder (optional Rx block)

Use minus or plus cylinder notation.

Prescription axis (°)

Axis linked to the entered prescription cylinder.

Vertex distance (mm)

Used for effective power estimates at the corneal plane.

Plotly Graph

The chart maps optical power across meridian angle. It updates after calculation.

Example Data Table

Case	Input Mode	Meridian A	Meridian B	Axis A	Mean Power	Cylinder	Classification
Optics Demo A	Radius	7.80 mm	7.50 mm	180°	44.13 D	1.73 D	With-the-rule
Optics Demo B	Power	42.75 D	44.00 D	90°	43.38 D	1.25 D	Against-the-rule
Optics Demo C	Power	43.20 D	45.10 D	45°	44.15 D	1.90 D	Oblique

Formula Used

1) Radius to power conversion

K = 1000 × (n − 1) / r(mm)

This converts meridian radius into dioptric power. The calculator uses the keratometric index and the entered radius in millimeters.

2) Astigmatism magnitude

Cylinder Magnitude = |Steep Power − Flat Power|

The difference between the two principal meridians gives the corneal or meridional astigmatism magnitude.

3) Mean optical power

Mean Power = (Flat Power + Steep Power) / 2

The mean power estimates the average focusing strength between both principal meridians.

4) Prescription spherical equivalent

SE = Sphere + (Cylinder / 2)

Spherical equivalent locates the circle of least confusion for a prescription-based estimate.

5) Focal interval of Sturm

Focal Interval = |Cylinder|

The focal interval measures the separation between the two line foci created by astigmatic optics.

6) Prescription transposition

New Sphere = Sphere + Cylinder New Cylinder = −Cylinder New Axis = Old Axis + 90°

The calculator also transposes the prescription between plus-cylinder and minus-cylinder notation.

7) Effective power at the corneal plane

F_effective = F / (1 − dF)

Here, d is vertex distance in meters. This estimate is useful for stronger prescriptions and engineering optics comparisons.

How to Use This Calculator

Select Radius mode if you know corneal radii, or Diopter mode if you already have principal powers.
Enter Meridian A axis. The calculator automatically places Meridian B at 90 degrees from it.
Provide the two meridian values. In radius mode, enter millimeters. In power mode, enter diopters.
Keep the keratometric index at 1.3375 unless your project uses a different model.
Optionally add Sphere, Cylinder, Axis, and Vertex Distance to analyze prescription behavior and transposition.
Click Calculate Astigmatism to show results above the form.
Review the summary metrics, result table, and the Plotly graph.
Use the export buttons to download your results as CSV or PDF.

FAQs

1) What does this astigmatism calculator estimate?

It estimates principal meridian power, cylinder magnitude, flat and steep axes, mean power, prescription spherical equivalent, focal interval, and transposed notation for engineering optics work.

2) Should I use radius mode or diopter mode?

Use radius mode when you have curvature in millimeters. Use diopter mode when keratometry or lens power data is already available in diopters.

3) Why is one meridian called flat and the other steep?

The flatter meridian has lower refractive power. The steeper meridian has higher refractive power because tighter curvature bends light more strongly.

4) What is with-the-rule astigmatism?

It usually means the steep meridian lies near 90 degrees. Against-the-rule lies near 180 degrees, while oblique falls between those zones.

5) What does spherical equivalent tell me?

Spherical equivalent averages the two prescription meridians. It estimates the location of the circle of least confusion rather than the full astigmatic interval.

6) Why is vertex distance included?

Vertex distance matters for stronger lenses because moving a lens changes its effective power at the corneal plane. This improves engineering estimates.

7) Can this replace a professional eye examination?

No. It is an educational and analytical tool. Clinical diagnosis and treatment still require licensed eye-care professionals and direct measurements.

8) What does the graph show?

The graph shows estimated power around meridian angle from 0 to 180 degrees. It makes the flat meridian, steep meridian, and mean behavior easier to compare.