The prescription at a glance
Most glasses prescriptions are a small grid: one row for each eye and one column for each measurement. The one below is made up. The numbers on the column headings match the sections of this guide.
Spectacle prescription (sample, not a real patient)
Values in dioptres, axis in degrees. Swipe the table for ADD and prism.
| Eye | SPH | CYL | AXIS | ADD | Prism | Base |
|---|---|---|---|---|---|---|
| ODright eye | −2.25 | −0.75 | 175 | +1.50 | none | none |
| OSleft eye | −1.75 | −1.00 | 10 | +1.50 | none | none |
PD 62 mm (31 / 31)
OD, OS and OU: which eye is which
OD is the right eye (oculus dexter), OS the left eye (oculus sinister) and OU both eyes (oculus uterque). Many prescriptions simply write R and L, or RE and LE.
The right eye is written first on almost every prescription, so a grid without labels still reads right, then left. Confirm it anyway before a lens is ordered: a swapped pair of lenses is a remake.
SPH: sphere
Sphere is the main lens power. It is measured in dioptres (D) and written in steps of 0.25. The sign says what kind of correction it is:
- Minus corrects short sight (myopia): distant things are blurred. Without glasses, a −2.00 eye sees sharply only out to about 50 cm, because the far point in metres is 1 divided by the power (1 ÷ 2.00 = 0.5 m).
- Plus corrects long sight (hyperopia): the eye has to focus harder than it should, most of all for close work.
You may also see PL or plano (no power, 0.00) and DS after a number, as in −1.75 DS: dioptres sphere, meaning that eye has no cylinder. A number written without a sign should be checked with the person who wrote it, never guessed.
CYL and AXIS: astigmatism
A cylinder value means the eye has astigmatism: it needs a different power in one direction than in the direction at right angles to it. An empty CYL box means there is none.
The axis is a direction, not a strength. It runs from 1 to 180 degrees (0 and 180 are the same line, and most prescriptions write 180), often after an ×, as in × 175. On the standard scale, 180 is horizontal and 90 is vertical, counted anticlockwise as the examiner faces the patient, for both eyes.
The axis is the direction in which the cylinder adds nothing. The full cylinder acts 90° away from it. For the right eye of the sample, −2.25 / −0.75 × 175:
| Direction | Power | Why |
|---|---|---|
| 175°, the axis | −2.25 | sphere only |
| 85°, 90° away | −3.00 | sphere + cylinder: −2.25 + (−0.75) |
Minus cylinder or plus cylinder: one lens, two ways to write it
Any prescription with astigmatism can be written with a minus cylinder or with a plus cylinder, and both describe exactly the same lens. Optometrists and optical labs mostly work in minus cylinder; many ophthalmologists write plus cylinder. Converting between the two is called transposition:
- New sphere = sphere + cylinder.
- New cylinder = the same number with the opposite sign.
- New axis = axis plus or minus 90, whichever keeps it between 1 and 180.
Worked through: +1.00 / −2.00 × 90 becomes −1.00 / +2.00 × 180, because +1.00 + (−2.00) = −1.00, the cylinder changes sign, and 90 + 90 = 180.
Transpose before comparing an old prescription with a new one, or before entering a plus-cylinder prescription where minus cylinder is expected. The transposition calculator does it for you, and the plus-to-minus cylinder converter handles a single lens.
Spherical equivalent
The spherical equivalent (SE) is the single sphere power that comes closest to a prescription with cylinder: the sphere plus half the cylinder. It is used when a sphere has to stand in for a small cylinder, for example in spherical soft contact lenses, and as a quick way to compare two prescriptions.
SE = SPH + CYL ÷ 2
For −2.25 / −0.75 × 175: SE = −2.25 + (−0.375) = −2.625 D.
Transposition never changes the spherical equivalent. The plus-cylinder form of the same lens, −3.00 / +0.75 × 85, gives −3.00 + 0.375 = −2.625 D again, which makes SE a handy check on a transposition done by hand. The spherical equivalent calculator works it out for you.
ADD: the reading addition
ADD is extra plus power for close work, needed once the eye's focusing range shrinks with age (presbyopia, usually noticed in the 40s). It is always plus, even when the sign is left off, typically between +0.75 and +3.00, and usually the same for both eyes.
For single-vision reading glasses, add it to the sphere and leave the cylinder and axis alone. With the sample's ADD of +1.50:
| Eye | Distance | Reading |
|---|---|---|
| OD | −2.25 / −0.75 × 175 | −0.75 / −0.75 × 175 |
| OS | −1.75 / −1.00 × 10 | −0.25 / −1.00 × 10 |
For bifocals and varifocals (progressives) the lab is given the distance prescription and the ADD separately, and the lens design builds the reading power in. Some prescriptions also give an intermediate (INT) power for screen distance. The distance-to-reading calculator does the arithmetic.
PD: pupillary distance
PD is the distance between the centres of the pupils, in millimetres; most adults measure between about 55 and 70 mm. It is written as one number (62) or as two monocular values measured from the centre of the nose (31 / 31, or 32 / 30.5 when the face is not symmetrical). Near PD, for reading glasses, is typically 3 to 4 mm smaller. Many prescriptions leave PD out, and the optician measures it when the frame is chosen.
PD matters because each lens's optical centre should sit in front of the pupil. When it does not, the lens bends light like a prism. Prentice's rule gives the amount: prism in prism dioptres = offset in centimetres × lens power in dioptres. A −4.00 lens with its centre 4 mm (0.4 cm) off gives 0.4 × 4.00 = 1.6Δ of prism the wearer never asked for. The stronger the lens, the more a PD error matters. For a lens with cylinder, use the power in the direction of the offset. The Prentice prism calculator works it out.
Prism and base
Most prescriptions leave these boxes empty. Prism, in prism dioptres (Δ), is prescribed to help the two eyes work together, for example to relieve double vision. One prism dioptre shifts the image by 1 cm at a distance of 1 m. The base is the direction the thick edge of the prism points:
- BU
- base up
- BD
- base down
- BI
- base in, towards the nose
- BO
- base out, towards the ear
Prism is often split between the eyes: 2Δ base in for each eye gives 4Δ base in altogether. Horizontal and vertical prism in the same eye can be combined into one with the compounding prism calculator.
Other things you may see
- VA (visual acuity)
- How well the eye sees on a letter chart, such as 6/6 (metres) or 20/20 (feet). 6/12 means the eye reads at 6 m what a typical eye reads at 12 m. It is a measurement, not a lens power.
- DV and NV
- Distance vision and near vision. Some prescriptions write the reading power out in full on an NV row instead of giving an ADD.
- BVD
- Back vertex distance: how far the back of the lens sits from the eye, in millimetres. Above about ±4.00 it changes the power that reaches the eye, so a lens fitted at a different distance needs a different power. The vertex distance calculator converts it.
- Contact lenses
- A glasses prescription is not a contact lens prescription. A contact lens prescription adds the base curve, diameter and lens type, and above about ±4.00 the power changes too: −6.00 in glasses worn 12 mm from the eye is about −5.60 at the eye.
Three prescriptions, read line by line
All three are made up, and each shows one of the situations above.
A. Short sight with astigmatism
R −4.50 / −1.25 × 20
L −4.00 / −1.50 × 160
PD 64
- Both spheres are minus: short-sighted in both eyes.
- Both eyes have astigmatism, written in minus cylinder. Right: −4.50 at 20° and −5.75 at 110°. Left: −4.00 at 160° and −5.50 at 70°.
- The axes 20 and 160 add up to 180: they mirror each other either side of vertical, which is common.
- The spherical equivalents are −5.125 and −4.75. Both eyes are above ±4.00, so a contact lens fitting would also allow for vertex distance.
B. Plus cylinder from an eye doctor
R +0.50 / +1.25 × 90
L PL / +1.50 × 85
- Written in plus cylinder. Transposed for a lab or system that expects minus cylinder: R +1.75 / −1.25 × 180, L +1.50 / −1.50 × 175.
- PL on the left is zero, so the new left sphere is 0.00 + 1.50 = +1.50.
- The spherical equivalents confirm it: right +1.125 and left +0.75, in both forms.
C. A first reading prescription
R +1.00 DS
L +1.25 / −0.50 × 95
ADD +2.00
- DS on the right: that eye has no astigmatism.
- Single-vision reading glasses: R +3.00 DS, L +3.25 / −0.50 × 95. The cylinder and axis do not change.
- Varifocals: order the distance powers with ADD +2.00.
In Asaan Optics, the prescription form has these same boxes (SPH, CYL, AXIS and VA for each eye, ADD and IPD), so a repeat order starts from the prescription exactly as it was written.
What a prescription leaves out
The lens material and index, coatings, the varifocal design and the frame are chosen at the optical counter, not written on the prescription. A prescription is not a diagnosis either: if the numbers changed and you want to know why, ask the person who examined your eyes.
Where to go next
- Transposition calculatorPlus cylinder to minus cylinder and back.
- Spherical equivalent calculatorSphere plus half the cylinder, done for you.
- All optical calculatorsVertex distance, prism, lens thickness and more.
- Optical shop software guideWhat it is, how to choose it, and a glossary.