Ophthalmic Optics & Visual Function
Every ophthalmic optics & visual function calculator on CalcEngines — unit converters, derived indices and interpretive tools, each with its formula, a worked example and the reference intervals it is judged against.
16 calculators in this section
- Corneal Astigmatism from Keratometry CalculatorSteep K minus flat K, in both cylinder forms with the axis each one takes, plus the radii behind the readings and why the 1.3375 that produced them is a convention and not a measurement.
- Corneal Radius to Dioptre ConverterK = 337.5 ÷ r, both ways, where 337.5 is (1.3375 − 1) × 1000 and 1.3375 is a convention rather than the cornea's refractive index. A 7.5 mm cornea is 45.00 D exactly — at that index.
- Cylinder Transposition CalculatorPlus cylinder to minus cylinder and back. Three steps, and the axis is the one that goes wrong: 170 + 90 is 260, which must become 80.
- ETDRS logMAR Letter Score CalculatorEvery letter is 0.02 logMAR and every line is 0.1, so logMAR = 1.70 − 0.02 × the letter score. The 4-metre score carries a 30-letter credit; leaving it out costs six lines.
- Lens Decentration and Minimum Blank SizeDecentration per eye is (frame PD − patient PD) ÷ 2, and the blank is the effective diameter plus twice that plus a working allowance. A 67 mm frame PD on a 62 mm patient needs 2.5 mm per lens.
- Near Addition from Amplitude of AccommodationThe working distance in dioptres, less the share of the amplitude the patient can sustain. Published guidance says a half or two thirds — so both answers are printed, with the gap between them.
- Oblique Meridian Lens Power CalculatorF = S + C·sin²(θ − axis). The power of −2.00 −1.00 × 180 at 45° is −2.50 D — neither the sphere nor the sphere plus the cylinder, which is the error this page exists to prevent.
- Obliquely Crossed Cylinders CalculatorTwo sphero-cylinders at any two axes, combined into one by power-vector addition and returned in minus-cylinder form. −2.00 −1.00 × 180 over plano −0.75 × 045 is −2.25 −1.25 × 018.
- Pantoscopic Tilt Compensation CalculatorMartin's rule of tilt: the sphere becomes D(1 + sin²θ/3) and a cylinder of D·tan²θ appears. A −10.00 D lens at 15° is −10.22 −0.72 × 180.
- Prentice’s Rule Prism CalculatorPrism dioptres = decentration in centimetres × lens power. A 4 mm centration error on a 4.00 D lens induces 1.60Δ — more than twice ANSI Z80.1's horizontal imbalance tolerance.
- Prism Dioptre to Degree Converter1Δ is 0.573°, 30Δ is 16.70° and 100Δ is exactly 45°: the relation is an arctangent, not a ratio. Both directions, with the error in the 0.57° rule of thumb computed across the range.
- Snellen to logMAR ConverterSnellen 6/12 is logMAR 0.301, decimal 0.5 and MAR 2 — the same measurement in four notations. Exact conversions both ways, in the 6 m and 20 ft forms, with the direction of each scale stated.
- Spectacle Magnification and AniseikoniaSM = shape factor × power factor. A +8.00 D lens at 12 mm magnifies 13.65%, a +5.00 D one 9.30%, and the 4.35% difference between them is the aniseikonia anisometropia produces.
- Spherical Equivalent CalculatorSphere plus half the cylinder. One number for a refraction with two principal meridians — and the number epidemiology counts myopia with, where moving the threshold 0.50 D nearly doubles the prevalence.
- Thick Lens Back Vertex Power CalculatorF₁ ÷ (1 − (t⁄n)F₁) + F₂, the exact form. A +9.40 / −4.70 lens 5.2 mm thick in polycarbonate is +5.00 D, not the +4.70 D its surfaces add to.
- Vertex Distance Compensation CalculatorA +10.00 D spectacle lens at 12 mm needs +11.36 D at the eye; a −10.00 D needs only −8.93. F ÷ (1 − dF), in both directions, with the point at which the change reaches a quarter dioptre computed rather than quoted.