Contact Lens Vertex Calculator for glasses to contacts, contacts to glasses or a new frame. It vertexes each meridian of a toric Rx, then rounds it to the steps lenses are made in.
Type the glasses Rx exactly as written, including the cylinder sign.
Left Eye (OS)
Clear the Sphere box to convert the right eye only.
Contact Lens Type
Spherical uses the SE. Rotation follows LARS: left adds, right subtracts.
Vertex Conversion Chart
| Glasses Power | Minus Contact | Plus Contact |
|---|---|---|
| ±4.00 | −3.75 (−3.82) | +4.25 (+4.20) |
| ±4.25 | −4.00 (−4.04) | +4.50 (+4.48) |
| ±4.50 | −4.25 (−4.27) | +4.75 (+4.76) |
| ±4.75 | −4.50 (−4.49) | +5.00 (+5.04) |
| ±5.00 | −4.75 (−4.72) | +5.25 (+5.32) |
| ±5.25 | −5.00 (−4.94) | +5.50 (+5.60) |
| ±5.50 | −5.25 (−5.16) | +6.00 (+5.89) |
| ±5.75 | −5.50 (−5.38) | +6.00 (+6.18) |
| ±6.00 | −5.50 (−5.60) | +6.50 (+6.47) |
| ±6.25 | −5.75 (−5.81) | +7.00 (+6.76) |
| ±6.50 | −6.00 (−6.03) | +7.00 (+7.05) |
| ±6.75 | −6.00 (−6.24) | +7.50 (+7.34) |
| ±7.00 | −6.50 (−6.46) | +7.50 (+7.64) |
| ±7.25 | −6.50 (−6.67) | +8.00 (+7.94) |
| ±7.50 | −7.00 (−6.88) | +8.00 (+8.24) |
| ±7.75 | −7.00 (−7.09) | +8.50 (+8.54) |
| ±8.00 | −7.50 (−7.30) | +9.00 (+8.85) |
| ±8.25 | −7.50 (−7.51) | +9.00 (+9.16) |
| ±8.50 | −7.50 (−7.71) | +9.50 (+9.47) |
| ±8.75 | −8.00 (−7.92) | +10.00 (+9.78) |
| ±9.00 | −8.00 (−8.12) | +10.00 (+10.09) |
| ±9.25 | −8.50 (−8.33) | +10.50 (+10.40) |
| ±9.50 | −8.50 (−8.53) | +10.50 (+10.72) |
| ±9.75 | −8.50 (−8.73) | +11.00 (+11.04) |
| ±10.00 | −9.00 (−8.93) | +11.50 (+11.36) |
| ±10.25 | −9.00 (−9.13) | +11.50 (+11.69) |
| ±10.50 | −9.50 (−9.33) | +12.00 (+12.01) |
| ±10.75 | −9.50 (−9.52) | +12.50 (+12.34) |
| ±11.00 | −9.50 (−9.72) | +12.50 (+12.67) |
| ±11.25 | −10.00 (−9.91) | +13.00 (+13.01) |
| ±11.50 | −10.00 (−10.11) | +13.50 (+13.34) |
| ±11.75 | −10.50 (−10.30) | +13.50 (+13.68) |
| ±12.00 | −10.50 (−10.49) | +14.00 (+14.02) |
Order power uses stock steps of 0.25 D up to ±6.00 D and 0.50 D beyond, exact power in brackets. The highlighted row is the strongest right-eye meridian.
Step-by-Step Calculation
- Contacts sit on the cornea, so d = 12 mm = 0.012 m and F′ = F ÷ (1 − d × F)
- OD meridian 180°: (−5.00) ÷ (1 − 0.012 × (−5.00)) = −4.717 D
- OD meridian 90°: (−6.50) ÷ (1 − 0.012 × (−6.50)) = −6.030 D
- OD exact: −4.72 −1.31 × 180
- OS meridian 8°: (−4.50) ÷ (1 − 0.012 × (−4.50)) = −4.269 D
- OS meridian 98°: (−5.25) ÷ (1 − 0.012 × (−5.25)) = −4.939 D
- OS exact: −4.27 −0.67 × 8
- Stock rounding: sphere to 0.25 D up to ±6.00 D and 0.50 D beyond, cylinder to −0.75, −1.25, −1.75, −2.25 or −2.75 D, axis to 10°, sphere picked to keep the meridian error smallest, toric sphere stocked from −9.00 to +6.00 D
- Order: OD −4.75 −1.25 × 180; OS −4.25 −0.75 × 10
Using the Contact Lens Vertex Calculator
The Contact Lens Vertex Calculator has three conversions. Glasses to Contacts is the default. Contacts to Glasses works the other way, and Glasses to New Frame handles a lens moving to a frame that sits closer or farther away.
Enter the vertex distance first. That is the gap between the back of the glasses lens and the front of the eye. 12 mm is the usual figure, and the calculator starts there. Your optician may write it on the Rx as BVD 12.
Type the right eye (OD) prescription exactly as written, including the minus or plus sign on the cylinder. The left eye (OS) sits in a folded section. Clear its sphere box if you only need one eye.
The Contact Lens Type section chooses between a toric lens, which corrects astigmatism, and a spherical lens that uses the spherical equivalent. It also sets the toric axis to stock 10° steps or to a custom 1° axis.
For torics, the same section has a Lens Rotation on Eye field. Enter how far a trial lens settles from its mark, plus for left and minus for right. The calculator then corrects the ordered axis with the LARS rule.
What the Results Show
The hero shows the power to order for both eyes. The default glasses Rx is OD −5.00 −1.50 × 180 and OS −4.50 −0.75 × 8. For it, the Contact Lens Vertex Calculator returns OD −4.75 −1.25 × 180 and OS −4.25 −0.75 × 10.
The first two cards give the exact power for each eye before any rounding. The right eye comes out at −4.72 −1.31 × 180. Each card also shows how far each meridian moved, here +0.28 D at 180° and +0.47 D at 90°.
The third card checks whether stock lenses fit. It shows the largest gap in any meridian between the exact power and the lens you order, measured as the lens sits on the eye. For the default Rx that gap is 0.03 D for the right eye and 0.07 D for the left.
The fourth card gives the spherical equivalent, which is sphere plus half the cylinder. Below the cards sit a vertex conversion chart, the step-by-step working and a note that changes with your result.
Vertex Conversion Formula
The Contact Lens Vertex Calculator rests on one idea. A glasses lens and a contact lens must focus light at the same point behind them. The contact sits about 12 mm closer to the eye, so it needs a slightly different power to reach that point. This is called vertex compensation.
$$F_c = \frac{F_s}{1 – d \cdot F_s}$$
Here Fs is the glasses power in diopters, Fc is the contact lens power, and d is the vertex distance in meters. A 12 mm vertex distance is entered as 0.012 m.
The formula comes from keeping the focal point fixed. A lens of power F has a focal length of 1 ÷ F. Moving it d closer to the eye shortens the distance to that point to (1 ÷ F) − d. The new power is the inverse of that distance.
Going from contacts back to glasses flips the sign of d. The Contacts to Glasses mode uses Fs = Fc ÷ (1 + d × Fc). The Glasses to New Frame mode uses the change in distance, d₁ − d₂, in place of d.
Worked Example: −6.00 D Glasses
Take a glasses power of −6.00 D at a 12 mm vertex distance. The bottom of the fraction is 1 − 0.012 × (−6.00) = 1.072. Dividing gives Fc = −6.00 ÷ 1.072 = −5.60 D.
Contacts are sold in 0.25 D steps up to ±6.00 D, so −5.60 D rounds to −5.50 D. The contact lens is half a diopter weaker than the glasses, even though both correct the same eye.
A +6.00 D glasses lens goes the other way. It becomes +6.47 D at the cornea and rounds to +6.50 D. Plus lenses gain power when moved toward the eye, while minus lenses lose it.
When Vertex Distance Matters
The shift grows quickly with power. At 12 mm a −2.00 D lens changes by only 0.05 D, which is far too small to notice. That is why low prescriptions often carry the same power in glasses and contacts.
The change reaches 0.125 D, half a quarter-step, at about 3.30 D for minus lenses and 3.17 D for plus lenses. It reaches a full 0.25 D step at about 4.70 D minus and 4.45 D plus.
So fitters usually start compensating beyond about ±4.00 D. When every meridian of your Rx stays inside ±4.00 D, the calculator says vertex barely matters and shows how small the largest shift is.
The vertex distance itself matters too. At −6.00 D, a 10 mm frame gives −5.66 D at the cornea and a 14 mm frame gives −5.54 D. At +6.00 D the same two frames give +6.38 D and +6.55 D.
Contact Lens Vertex Chart
The chart below uses a 12 mm vertex distance, the most common value on a prescription. It shows the exact contact lens power and the stock power you would order, for minus and plus glasses powers.
| Glasses Power (D) | Minus Exact | Minus Order | Plus Exact | Plus Order |
|---|---|---|---|---|
| ±4.00 | −3.82 | −3.75 | +4.20 | +4.25 |
| ±4.50 | −4.27 | −4.25 | +4.76 | +4.75 |
| ±5.00 | −4.72 | −4.75 | +5.32 | +5.25 |
| ±5.50 | −5.16 | −5.25 | +5.89 | +6.00 |
| ±6.00 | −5.60 | −5.50 | +6.47 | +6.50 |
| ±6.50 | −6.03 | −6.00 | +7.05 | +7.00 |
| ±7.00 | −6.46 | −6.50 | +7.64 | +7.50 |
| ±7.50 | −6.88 | −7.00 | +8.24 | +8.00 |
| ±8.00 | −7.30 | −7.50 | +8.85 | +9.00 |
| ±8.50 | −7.71 | −7.50 | +9.47 | +9.50 |
| ±9.00 | −8.12 | −8.00 | +10.09 | +10.00 |
| ±10.00 | −8.93 | −9.00 | +11.36 | +11.50 |
| ±11.00 | −9.72 | −9.50 | +12.67 | +12.50 |
| ±12.00 | −10.49 | −10.50 | +14.02 | +14.00 |
Order powers follow the steps in the ACUVUE Technical Specification Guide. Lenses come in 0.25 D steps up to ±6.00 D and 0.50 D steps beyond. That is why −8.00 D glasses give a −7.50 D order rather than −7.25 D.
The Contact Lens Vertex Calculator builds its own vertex distance chart at whatever distance you enter. It runs from ±4.00 D to ±12.00 D in quarter steps and highlights the row closest to your right eye. Print / PDF saves that chart as a contact lens vertex chart PDF.
Toric Contact Lens Vertex Conversion
A toric prescription has two powers, one in each principal meridian. Vertexing only the sphere and keeping the cylinder is a common mistake. The cylinder also changes, because each meridian shifts by a different amount.
The Contact Lens Vertex Calculator converts each meridian on its own and then rebuilds the cylinder. Take glasses at −6.00 −2.00 × 170. The 170° meridian is −6.00 D and the 80° meridian is −6.00 + (−2.00) = −8.00 D.
At 12 mm those become −5.60 D and −7.30 D. The contact lens Rx is the first meridian as the sphere and the difference as the cylinder, so −5.60 −1.70 × 170. The axis does not change.
The calculator then rounds to stock toric powers. The cylinder snaps to the nearest stock value, −1.75 D. The order is −5.50 −1.75 × 170, within 0.10 D of the exact power in every meridian.
The sphere is not rounded blindly. When the cylinder snaps, the calculator tries the nearby stock sphere steps, including the one that keeps the spherical equivalent. It keeps whichever gives the smallest error in any meridian.
Prescriptions written in plus cylinder are converted to the usual minus-cylinder form before ordering. You do not need to transpose them first, as long as you type the cylinder sign as written.
Stock Toric Limits
ACUVUE OASYS for ASTIGMATISM is listed with cylinders of −0.75, −1.25, −1.75, −2.25 and −2.75 D. Its axes run from 10° to 180° in 10° steps. The calculator rounds to that same cylinder list and axis grid.
The same listing runs from −9.00 to +6.00 D sphere. Past that range the calculator marks the lens as a custom toric. Glasses at +7.00 −1.25 × 90 give +7.64 −1.47 × 90 at the cornea, so the order becomes a custom +7.75 −1.50 × 90.
When the cylinder at the cornea passes −2.75 D, the calculator stops calling the lens stock. A strong Rx such as −8.00 −4.25 × 45 at 14 mm becomes −7.19 −3.26 × 45. That needs a made-to-order toric or a rigid gas permeable lens.
Lens Rotation and the LARS Rule
A soft toric often settles a little away from where it was designed to sit. Fitters read the rotation from the marks on the trial lens, as seen from their side of the slit lamp. The LARS rule then says Left Add, Right Subtract.
If the lens rotates 10° to the left, 10° is added to the ordered axis. If it rotates 15° to the right, 15° is taken away. The new lens then rotates by the same amount and lands on the axis the eye needs.
Take the −6.00 −2.00 × 170 Rx with a lens that rotates 15° right. The axis becomes 155°, which rounds to the stock 160°. On the eye it sits at 175°, so the worst meridian error is 0.23 D.
Without the correction, the lens would sit at 155° and the error would reach 0.52 D. For a 10° left rotation the calculator orders axis 180°, which sits at 170° on the eye and keeps the error at 0.10 D.
Spherical Equivalent Instead of a Toric
Low astigmatism is often fitted with a spherical lens at the spherical equivalent. That is the sphere plus half the cylinder. Choose Spherical in the Lens Design menu and the calculator orders that single power.
Glasses at −3.00 −0.75 × 180 give an exact contact power of −2.90 −0.69 × 180 at 12 mm. The spherical equivalent is −3.24 D, which orders as −3.25 D, leaving 0.69 D of cylinder uncorrected.
When 0.75 D or more of cylinder would stay uncorrected, the calculator warns that a spherical lens leaves blur. The Angular Resolution Calculator puts a 3 mm pupil’s diffraction limit near 46 arcseconds, far finer than uncorrected astigmatism allows.
Contacts to Glasses and Frame Changes
The Contact Lens Vertex Calculator also works as a vertex conversion calculator in either direction. In Contacts to Glasses mode it adds back the power the contact lost. A −5.50 D contact lens becomes −5.89 D at 12 mm, which rounds to −6.00 D for glasses.
Use the result only as a starting point. A glasses Rx comes from a refraction, and the final power can differ slightly from the converted value once frame fit and tilt are known.
Glasses to New Frame acts as a vertex correction calculator for frames that sit at a different distance. A +8.00 D lens moved from 12 mm to 16 mm needs +7.75 D to give the same focus. A −10.00 D lens moved from 14 mm to 10 mm needs −9.62 D.
High-power wearers often notice this with binoculars too. Glasses hold the eye farther back, so they need binoculars with long eye relief. Contacts remove that gap, which helps when you read a mil reticle for the Binoculars Range Calculator.
Diopters and Focal Length
A diopter is the inverse of focal length in meters. A −5.00 D lens has a focal length of −200 mm, and a +4.00 D lens focuses at 250 mm. The Aperture Area Calculator uses the same focal length idea for camera and telescope lenses.
This is why vertex distance matters more at high power. A 12 mm shift is small next to a 2 m focal length, which is 0.50 D. It is large next to a 100 mm focal length, which is 10.00 D. The Optics Calculators hub has more tools for lenses and light.
Brand Steps and Toric Calculators
Lens makers publish their own power ranges and steps. Johnson & Johnson, CooperVision and Bausch + Lomb each offer fitting tools for their toric lenses, such as CooperVision’s ToriTrack calculator. Each one is built around that brand’s own lens range.
Ranges also differ between products from the same maker. ACUVUE OASYS 1-Day for ASTIGMATISM, for example, offers −2.25 D cylinder only at selected axes, while the two-week lens offers every 10° step. Check the exact product before ordering.
The Contact Lens Vertex Calculator works across brands. It uses the common stock steps and shows the exact power next to the order. That makes it easy to check a brand tool’s result, or to see how far a stock lens sits from the ideal power.
Reading and Ordering Your Rx
These answers cover what people ask most about vertexing a prescription. They run from reading BVD on an Rx to whether a converted power can be used to order contacts online.
What does BVD 12 mean on an eye prescription?
BVD stands for back vertex distance. BVD 12 means the glasses lens was measured 12 mm in front of the cornea during the eye test. It is the distance you enter in the calculator.
If your Rx shows no BVD, 12 mm is the usual starting value. Frames that sit very close or very far can move the result for strong prescriptions. Above about ±6.00 D, measure the actual fit.
Why is my contact lens power lower than my glasses?
For a minus (nearsighted) prescription, the contact sits closer to the eye. A weaker minus lens reaches the same focal point from there. So −6.00 D glasses become about −5.50 D contacts at 12 mm.
For a plus (farsighted) prescription the opposite happens. The contact needs more plus, so +6.00 D glasses become about +6.50 D contacts. Below about ±4.00 D the two powers usually stay the same.
Can I use a contact lens vertex calculator online to order contacts?
No. The Contact Lens Vertex Calculator gives a starting power only. A contact lens prescription also sets the brand, base curve and diameter. It needs a fitting to check how the lens sits and moves on the eye.
In the United States, the FTC Contact Lens Rule requires prescribers to give patients a copy of their contact lens prescription after a fitting. That copy, not a converted glasses Rx, is what online sellers verify before they ship.
Does vertexing change the cylinder axis?
No. The axis stays the same, because the meridians keep their direction when the lens moves closer. Only the powers in each meridian change, which changes both the sphere and the cylinder.
The calculator may still show a different axis on the order. That happens when a stock toric only comes in 10° steps, so an axis of 8° is ordered as 10°. Choose Custom, 1° Steps to keep the exact axis.
Does vertex distance matter for low prescriptions?
Very little. A −3.00 D lens changes by only 0.10 D at 12 mm, less than half a quarter-step. The calculator shows a note when every meridian stays inside ±4.00 D.
Astigmatism can still need a look at lower powers. The stronger meridian may pass ±4.00 D even when the sphere does not, so a −3.50 −1.00 Rx is worth converting meridian by meridian.