Calculate IOL power with the original Holladay 1 formula from axial length, keratometry and an A-constant or surgeon factor. For education only.

Original conversion: SF = 0.5663 × A − 65.60. Constants are formula and measurement specific.

Default 0 D is a chosen emmetropic target, not a patient measurement.

Default 12 mm; use the distance appropriate to the refraction being modeled.

Optional settings

Important: This calculator is for educational use by ophthalmology professionals and students only. It is not medical advice and does not replace validated surgical planning software (IOL Master, LENSTAR, etc.). IOL selection must be verified by a licensed ophthalmologist using optimized lens constants from the manufacturer, ULIB, or IOLCon. If you experience eye pain, sudden vision loss, flashes, or floaters, seek emergency ophthalmic care immediately.

Related Calculators

Holladay 1 Formula

The Holladay 1 formula calculates IOL power in three steps: corneal radius derivation from keratometry, effective lens position (ELP) prediction via Fyodorov's corneal height geometry, and final power from thin-lens vergence optics.

Corneal radius and Fyodorov corneal height:

r=(337.5) / (K); rg=max(r,7); AG=min((12.5AL) / (23.45),13.5); H=0.56+rg−√(rg2−AG2/4)

Effective lens position and vertex-corrected refraction:

ELP=SF+H; ALm=AL+0.200; TCP=(1000) / (3r); Rc=(R) / (1−VR/1000)

IOL power (vergence formula):

P=(1336) / (ALm−ELP)−(1336(TCP+Rc)) / (1336−ELP(TCP+Rc))

Variables:

  • AL = measured ultrasonic axial length (mm) in the original model; ALm = AL + 0.200 mm. Do not apply that adjustment indiscriminately to optical-biometry measurements.
  • K = average corneal power (D); mean of flat (K1) and steep (K2) meridians from keratometry or topography
  • R = target refraction at spectacle plane (D); 0.00 D for emmetropia, -0.25 D for slight myopic target
  • SF = surgeon factor (mm), the modeled iris-plane-to-IOL-plane distance. The original Table 1 conversion is SF = 0.5663 × A − 65.60. Constants are formula and measurement specific; this arithmetic does not optimize or validate a constant for a patient or lens.
  • r = 337.5/K in mm; rg is the geometry radius with a 7 mm lower bound; AG is the axial-length-dependent angle-to-angle estimate capped at 13.5 mm. TCP is the model corneal power using refractive index 4/3.
  • H = Fyodorov corneal height (mm); geometric estimate of the anterior segment depth offset from corneal curvature
  • ELP = predicted effective lens position (mm); Rc = target refraction corrected to the corneal plane using entered vertex distance V (mm, default 12); 1336 = aqueous/vitreous refractive index 1.336 × 1000.

What is the Holladay 1 Formula?

Holladay and colleagues published the original system in 1988. It estimates lens position from axial length, corneal curvature and a surgeon factor, then applies vergence optics. The equations above follow that paper’s Appendix, rather than a fixed-diameter corneal-height approximation. Primary source: A three-part system for refining intraocular lens power calculations, J Cataract Refract Surg 14, 17–24.

The Surgeon Factor (SF) is the Holladay 1 lens constant. It represents the physical distance from the pseudophakic iris plane to the principal plane of the IOL, making it anatomically meaningful rather than a pure regression offset. SF is not interchangeable with the SRK/T A-constant, Haigis a0, or Hoffer Q pACD; each constant is formula-specific and must be sourced from the manufacturer or an optimized database such as ULIB or IOLCon.

The original Appendix defines axial length as an ultrasonic measurement. This reproduction does not implement later axial-length adjustments, modern device-specific calibration, toric planning or patient-specific formula selection. Its mathematical results and comparison grid must not be used as a surgical recommendation.

How to Calculate IOL Power Using the Holladay 1 Formula

The following steps outline how to calculate IOL power using the Holladay 1 formula:

  1. For this original-model educational calculation, enter measured ultrasonic axial length (AL). Do not substitute optical-biometry data without an independently validated implementation.
  2. Measure average keratometry (K): mean of flat (K1) and steep (K2) meridians in diopters.
  3. Determine target refraction (R): typically 0.00 D for emmetropia or a slight myopic target such as -0.25 D.
  4. Obtain the Surgeon Factor (SF) from the lens manufacturer, ULIB, or IOLCon. If only the A-constant is available, apply: SF = 0.5663 x A - 65.60.
  5. Calculate corneal radius: r = 337.5 / K.
  6. Set geometry radius rg = max(r, 7 mm) and AG = min(12.5 × AL/23.45, 13.5 mm). Calculate H = 0.56 + rg − √(rg² − AG²/4).
  7. Calculate predicted ELP: ELP = SF + H.
  8. Apply the entered vertex correction: Rc = R/(1 − V × R/1000). The default V is 12 mm; a zero target gives Rc = 0 D.
  9. Set ALm = AL + 0.200 mm and TCP = 1000/(3r). Calculate P = 1336/(ALm − ELP) − 1336(TCP + Rc)/(1336 − ELP(TCP + Rc)).
  10. Compare the unrounded mathematical power with the selected 0.25, 0.50 or 1.00 D grid and adjacent grid points. Actual lens availability and clinical suitability require independent verification.

Example Problem:

Axial Length (AL) = 23.50 mm

Keratometry (K) = 44.00 D

Target Refraction (R) = 0.00 D (emmetropia)

A-constant = 118.4; SF = 0.5663 × 118.4 − 65.60 = 1.44992 mm

r = 337.5 / 44.00 = 7.6705 mm

Geometry radius = 7.67045455 mm; AG = 12.52665245 mm; H = 3.80251851 mm.

ELP = 1.44992 + 3.80251851 = 5.25243851 mm; adjusted AL = 23.70000 mm; TCP = 43.45679012 D.

Rc = 0.00 / (1 - 0) = 0.00 D

Using full precision in the original-model equation gives P = 20.01031345 D. Intermediate values displayed above are rounded.

Nearest 0.50 D comparison grid point = 20.00 D. As an independent check, the original paper’s Appendix example uses K = 46 D, AL = 22 mm, SF = 0.5 mm, V = 12 mm and target −0.5 D, producing 21.45970 D.