HOMA-B Calculator
HOMA-B Calculator
Estimate beta-cell function from fasting glucose and insulin, with the derivation of the 360 and 63 constants and why the equation fails near a glucose of 63 mg/dL.
HOMA-B
Fasting pair → beta-cell %Fasting glucose 105 mg/dL, fasting insulin 12 µIU/mL
Formula
HOMA-B (%) = 20 × insulin (µIU/mL) ÷ [glucose (mmol/L) − 3.5]
- 360 and 63
- the conventional-unit constants; multiplying the SI form through by 18 gives 20 × 18 = 360 and 3.5 × 18 = 63, so the two forms are the same equation
- 20 and 3.5
- the SI constants, scaled so that a normal young adult scores 100%
- 100%
- defined as the reference young-adult population of the original model, not a clinical target and not a proportion of surviving beta cells
- denominator
- as fasting glucose approaches 63 mg/dL the denominator approaches zero and the result diverges, so the index is not interpretable in hypoglycaemia
Worked example
Fasting glucose 105 mg/dL, fasting insulin 12 µIU/mL
105 − 63 = 42
360 × 12 = 4,320
4,320 ÷ 42 = 103% beta-cell function
In SI units: 105 ÷ 18 = 5.83 mmol/L; 20 × 12 ÷ (5.83 − 3.5) = 103 — the same answer
Between 100 and 200 → around the reference population
Reading HOMA-B alongside HOMA-IR
| HOMA-B | HOMA-IR | Interpretation |
|---|---|---|
| High | High | Compensated insulin resistance — secretion has risen to hold glucose down, and is currently succeeding |
| Normal or falling | High | Failing compensation; the pattern that marks progression towards type 2 diabetes |
| Low | Low | Primary secretory failure rather than resistance — consider type 1 diabetes, latent autoimmune diabetes in adults, or pancreatic disease |
| Low | High | Advanced type 2 diabetes, with both resistance and exhausted secretion |
The same equation in two unit systems
| Conventional | SI | |
|---|---|---|
| Glucose unit | mg/dL | mmol/L |
| Numerator constant | 360 | 20 |
| Subtracted constant | 63 | 3.5 |
| Worked example | 360 × 12 ÷ (105 − 63) = 103 | 20 × 12 ÷ (5.83 − 3.5) = 103 |
What 100% means, and why the denominator matters
HOMA-B estimates fasting beta-cell function from the same pair of measurements as HOMA-IR. The SI form is 20 × insulin in µIU/mL divided by glucose in mmol/L minus 3.5. Multiplying through by 18, the factor between mmol/L and mg/dL, gives the conventional form used here: 360 × insulin divided by glucose in mg/dL minus 63. The constants 360 and 63 are not separate empirical numbers; they are 20 and 3.5 expressed for mg/dL, and the two equations return identical results.
The output is a percentage, and the percentage is the source of most misreadings. It is not the proportion of surviving beta cells and it is not a target. One hundred per cent is defined as the fasting secretory function of the reference young-adult population of the original model, so a result of 103% means this patient's fasting insulin output, for their prevailing glucose, resembles that reference group. A result well above 100% is not better health; with a raised HOMA-IR it usually means the beta cells are working hard to compensate for insulin resistance.
That compensation is the pattern worth tracking. Early insulin resistance is met by increased secretion, so HOMA-B rises while fasting glucose stays normal. Progression to type 2 diabetes is marked by HOMA-B falling as glucose climbs, because the compensation is failing rather than because resistance has improved. A single value describes a moment; the trajectory of the pair, measured on the same assay, is what actually shows what is happening.
The equation has a hard mathematical limit. As fasting glucose approaches 63 mg/dL, or 3.5 mmol/L, the denominator approaches zero and the result diverges towards infinity; below that value it turns negative and becomes nonsense. HOMA-B is therefore uninterpretable in hypoglycaemia, which is precisely the setting where a question about excessive insulin secretion most often arises — an insulinoma is investigated with a supervised fast and paired insulin, C-peptide and glucose, not with this index. The same caveats as HOMA-IR apply otherwise: a genuinely fasting sample is required, exogenous insulin invalidates it, and insulin assays are not standardised between laboratories.
Frequently asked questions
How is HOMA-B calculated?
Multiply fasting insulin in µIU/mL by 360 and divide by fasting glucose in mg/dL minus 63. With glucose in mmol/L the equivalent form is 20 × insulin divided by glucose minus 3.5. Both constants differ by a factor of 18, so the two forms agree exactly.
Does 100% mean all my beta cells are working?
No. One hundred per cent is defined as the fasting secretory function of the reference young-adult population in the original 1985 model. It describes how this patient's fasting insulin output compares with that group for the prevailing glucose, and it is not a count of surviving beta cells or a treatment target.
Is a high HOMA-B a good result?
Not on its own. A high HOMA-B with a high HOMA-IR is compensated insulin resistance: secretion has increased to hold glucose down. That compensation is what fails as type 2 diabetes develops, so a falling HOMA-B alongside a rising glucose is the pattern that marks progression.
Why does the calculator refuse a glucose below 64 mg/dL?
The denominator is glucose minus 63 mg/dL, so it reaches zero at 63 and the result diverges. Below that the value turns negative and means nothing. The index cannot be used in hypoglycaemia.
Can HOMA-B be used to investigate an insulinoma?
No. Insulinoma is investigated with a supervised 72-hour fast and paired glucose, insulin, C-peptide and proinsulin measurements taken during documented hypoglycaemia. HOMA-B is undefined in that setting because the denominator collapses.
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References
- Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC. Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man. Diabetologia. 1985;28(7):412–419.
- Levy JC, Matthews DR, Hermans MP. Correct homeostasis model assessment (HOMA) evaluation uses the computer program. Diabetes Care. 1998;21(12):2191–2192.
- Wallace TM, Levy JC, Matthews DR. Use and abuse of HOMA modeling. Diabetes Care. 2004;27(6):1487–1495.