IOL power formulae predict the lens power that gives the target postoperative refraction (see Biometry for the measurements)
Inputs: axial length (AL), keratometry (K), the lens constant and the target refraction. Newer formulae add anterior chamber depth (ACD), lens thickness, white-to-white diameter, age and the preoperative refraction
The hardest part is predicting the effective lens position (ELP): where the IOL will sit after surgery

## The vergence formula

Theoretical formulae treat the cornea and IOL as two thin lenses. For emmetropia (AL and ELP in mm, n = 1.336):

P = 1336 ÷ (AL − ELP) − 1336 ÷ (1336 ÷ K − ELP)
Worked example: AL 23.5 mm, K 43.5D, ELP 5.25 mm. 1336 ÷ 18.25 = 73.21; 1336 ÷ 43.5 = 30.71 mm, minus 5.25 = 25.46 mm, and 1336 ÷ 25.46 = 52.47. P = 73.21 − 52.47 = +20.7D

A more posterior IOL (larger ELP) needs more power; a more anterior one needs less (see Biometry)

## Regression and formula generations

Worked example: A-constant 118.4, AL 23.5 mm, K 43.5D. P = 118.4 − 58.75 − 39.15 = +20.50D, close to the vergence result above
It shows the sensitivities: 1 mm of AL ≈ 2.5D of IOL power, and 1D of K ≈ 0.9D of IOL power
It is inaccurate in short and long eyes, and is no longer used

Generation	Examples	How ELP is predicted
First	SRK I, Binkhorst	Regression only, or a fixed ELP
Second	SRK II	A-constant adjusted for AL
Third	SRK/T, Hoffer Q, Holladay 1	From AL and K
Fourth	Haigis (three constants, uses ACD), Holladay 2, Olsen	From AL, K, ACD and other variables
Newer	Barrett Universal II, Kane, Hill-RBF, EVO	Thick-lens, ray-tracing or artificial intelligence methods

Short eyes (AL under about 22 mm): Hoffer Q or Haigis among the older formulae
Long eyes (AL over about 26 mm): SRK/T. Older formulae tend to leave long eyes hypermetropic; an AL adjustment (Wang–Koch) helps
Newer formulae (e.g. Barrett Universal II, Kane) perform well across all axial lengths

## Lens constants

The A-constant (or ACD constant or surgeon factor) is specific to the IOL model and its expected position. Anterior chamber IOLs have lower A-constants than posterior chamber IOLs
In SRK formulae, a 1-unit change in A changes the IOL power by 1D
Constants should be optimised from a surgeon's own outcomes, and differ between optical and ultrasound biometry
Ametropic targets: each 1D of IOL power changes the spectacle refraction by about 0.7D. For example, a −0.50D target needs about 0.75D more IOL power than emmetropia

## Special situations

Keratometric index error: 1.3375 no longer fits the altered anterior/posterior ratio
Instrument error: the keratometer measures a zone outside the flattened centre
Formula error: third-generation formulae predict a shallow ELP from the flat K
After myopic ablation, corneal power is overestimated and the IOL is too weak: a hypermetropic surprise. After hypermetropic ablation, a myopic surprise
Use dedicated methods: Haigis-L, Barrett True-K, Shammas, total keratometry, or online calculators that average several methods

Sound travels more slowly in oil (about 980 m/s against 1,532 m/s in vitreous), so ultrasound overestimates AL unless corrected. Optical biometry is preferred
If the oil will stay, oil behind a biconvex IOL reduces its power: add about +3D

Sulcus placement: a lens planned for the bag sits further forward in the sulcus, so reduce its power, usually by 0.5–1.0D
Children: the eye will grow and become more myopic, so a hypermetropic target is chosen, depending on age
Toric IOLs: the IOL cylinder is about 1.5 times the corneal astigmatism to be corrected. Planning must include posterior corneal astigmatism and surgically induced astigmatism (see Astigmatism)

Common causes of refractive surprise: wrong AL (most often), wrong K, wrong lens constant, the wrong IOL implanted, and an unexpected lens position
AL error is the biggest source: 1 mm of AL error gives about 2.5–3D of refractive error
Ultrasound biometry measures to the internal limiting membrane; optical biometry measures to the retinal pigment epithelium. Contact ultrasound can compress the cornea and give a falsely short AL

Check both eyes together: an inter-eye difference in AL or K out of keeping with the refraction suggests a measurement error
Optical biometry may fail through dense cataract or poor fixation; immersion ultrasound is then preferred to contact ultrasound