Contact Lens Vertex Calculator

Convert a glasses (spectacle) prescription to an estimated contact lens prescription by adjusting for vertex distance, including cylinder and axis. You can also use it for frame changes by entering a different final vertex distance and choosing rounding.

Conversion type

Choose what you are converting. Most people use Spectacles to contacts. Frame change means glasses to glasses with a different distance from the eye.

Sphere (D)

The main lens power. Use negative for myopia (minus) and positive for hyperopia (plus). Example: -5.00 or +2.50.

Cylinder (D)

Astigmatism power. If you have no cylinder, enter 0.00. Keep the sign shown on your prescription.

Axis (degrees)

Astigmatism direction from 1 to 180. If cylinder is 0.00, axis is ignored.

Initial vertex distance (mm)

Distance from the back of the glasses lens to the cornea for the original prescription. Typical glasses values are about 12 to 14 mm. For a contact lens, use 0 mm.

Advanced options

Vertex distances

Final vertex distance (mm)

Distance for the new lens position. For contact lenses, this is 0 mm. For a new glasses frame, enter the new measured vertex distance.

Rounding

Rounding step (D)

How to round the final powers. Many lenses come in 0.25 D steps. Choose Exact to see raw math.

Rounding rule

Nearest rounds to the closest step. Down (more minus / less plus) and Up (less minus / more plus) are sometimes used for trial lens selection, but your clinician decides.

Prescription format

Output cylinder format

Choose whether to keep the same cylinder sign as the input, or transpose to plus-cylinder form. This changes how the prescription is written, not the optics.

Tip: If your cylinder on the paper Rx is positive, choose “Keep input sign” to see plus-cylinder output.

Calculating…

Converted sphere (exact) (D)

–

Calculated after vertex adjustment, before rounding.

Converted cylinder (exact) (D)

–

Calculated by adjusting each principal meridian separately.

Axis (degrees)

–

Axis stays the same because we only change power, not direction.

Principal meridian power at axis (exact) (D)

–

One principal meridian (the axis meridian).

Principal meridian power 90 degrees away (exact) (D)

–

The other principal meridian (axis plus 90 degrees).

Change in axis meridian power (new minus old) (D)

–

Negative means more minus (or less plus) in that meridian.

Change in 90-deg meridian power (new minus old) (D)

–

Signed change for the second meridian.

Converted sphere (rounded) (D)

–

Rounded to your chosen step and rule (or Exact if you chose no rounding).

Converted cylinder (rounded) (D)

–

If rounding makes cylinder 0.00, the axis is not clinically meaningful.

Notes and warnings

–

Estimates only. Confirm with an eye care professional.

Did we solve your problem today?

How to use our Contact Lens Vertex Calculator

Choose a conversion type (most people use Spectacles to contacts, often 12 mm to 0 mm).
Enter Sphere (D) exactly as written on the prescription (use minus for myopia and plus for hyperopia).
Enter Cylinder (D). If you have no astigmatism, enter 0.00.
If Cylinder is not 0.00, enter Axis (degrees) from 1 to 180 (if Cylinder is 0.00, Axis is ignored).
Enter the Initial vertex distance (mm) for the original lens position (typical glasses are around 12 to 14 mm).
Open Advanced options if needed and enter Final vertex distance (mm) (use 0 mm for contact lenses, or a different value for a new glasses frame).
In Advanced options, pick a rounding step (or Exact) and a rounding rule (Nearest, Up, or Down).
Choose an output cylinder format (keep the input sign or transpose to plus-cylinder form).
Click Calculate to see the exact converted sphere/cylinder, the two principal meridian powers, how much each meridian changed, and the rounded result.

Definitions

Vertex distance (mm): The gap from the back of a glasses lens to the front of your eye. Contacts sit on the eye, so their vertex distance is treated as 0 mm.

Diopter (D): A unit of lens power. Higher absolute values (like -8.00 D or +6.00 D) are more sensitive to vertex distance changes.

Sphere (D): The main focusing power for nearsightedness (minus) or farsightedness (plus).

Cylinder (D): Extra power for astigmatism. It affects one direction more than the other.

Axis (degrees): The direction (1 to 180) that tells where the cylinder has no effect. It is used only when Cylinder is not 0.00.

Principal meridians: The two perpendicular directions of lens power: one along the axis, and one 90 degrees away. This calculator adjusts each one separately, then converts back to sphere/cylinder/axis. [2]

Transpose (plus-cylinder vs minus-cylinder): Two different ways to write the same optics. Transposing changes the written numbers, not the actual lens effect.

Methodology

What this calculator is doing

Glasses sit a few millimeters in front of the eye, but contact lenses sit on the eye. Moving a lens closer or farther changes its effective power. Vertex compensation estimates the new power after a change in vertex distance. [1]

Step 1: Handle cylinder sign (internal standard)

This calculator does the meridian math in minus-cylinder form.

If your input Cylinder is already negative (or 0.00), it is treated as minus-cylinder.

If your input Cylinder is positive (plus-cylinder), the calculator first transposes it to an equivalent minus-cylinder prescription (same optics) before computing meridians, and then (optionally) transposes back for display.

Sphere_minus = Sphere_plus + Cylinder_plus

Cylinder_minus = -Cylinder_plus

Axis_minus = (Axis_plus + 90) mod 180, with 0 treated as 180

Step 2: Convert sphere/cylinder to the two principal meridian powers

The axis meridian equals the sphere. The meridian 90 degrees away equals sphere plus cylinder. [2]

F_axis_old = Sphere

F_orth_old = Sphere + Cylinder

Step 3: Vertex compensate each meridian (mm to m)

Convert millimeters to meters and compute the distance change.

d_initial_m = vertex_initial_mm / 1000

d_final_m = vertex_final_mm / 1000

delta_d_m = d_initial_m - d_final_m

Apply the standard vertex compensation to each meridian. [1]

F_new = F_old / (1 - delta_d_m * F_old)

F_axis_new = F_axis_old / (1 - delta_d_m * F_axis_old)

F_orth_new = F_orth_old / (1 - delta_d_m * F_orth_old)

If a denominator is 0 (or extremely close to 0), the result is not computable, and the calculator shows an error instead of an infinite value.

Step 4: Convert the new meridians back to sphere/cylinder/axis

Sphere_out_minus = F_axis_new

Cylinder_out_minus = F_orth_new - F_axis_new

Axis_out = Axis_in

The axis stays the same because vertex compensation changes strength, not direction.

Step 5: Changes (deltas) reported in the results

Each delta is the compensated meridian minus the original meridian. Negative means more minus (or less plus) in that direction.

Delta_axis = F_axis_new - F_axis_old

Delta_orth = F_orth_new - F_orth_old

Step 6: Optional transpose for display

If you choose plus-cylinder output, the calculator transposes the computed minus-cylinder output to plus-cylinder form (same optics).

Sphere_out_plus = Sphere_out_minus + Cylinder_out_minus

Cylinder_out_plus = -Cylinder_out_minus

Axis_out_plus = (Axis_out_minus + 90) mod 180, with 0 treated as 180

Step 7: Rounding (optional)

If you choose a step like 0.25 D, rounding is applied after all exact calculations (rounded values do not feed back into the math).

Rounded = round_rule(Exact / step) * step

Nearest rounds to the closest step. Up means toward more plus (or less minus). Down means toward more minus (or less plus).

Notes on interpretation

Vertex effects are usually small at low powers and larger at high absolute powers or large vertex changes. If rounding removes cylinder (for example, cylinder rounds to 0.00), the display may no longer reflect available toric lens choices, so treat the rounded result as a practical estimate to discuss with a clinician.