HOMA-IR calculator (with HOMA-%B)
Estimate insulin resistance (HOMA-IR) and beta-cell function (HOMA-%B) from one fasting glucose and one fasting insulin, with the formulas Matthews and colleagues published in 1985. Glucose can be in mg/dL or mmol/L and insulin in µU/mL or pmol/L.
Guides
- HOMA-IR normal range: why there is no single numberWhy HOMA-IR has no single normal range: what studies in Japan, Spain, Italy, Brazil and Texas found, how fasting and assays change it, and its limits.
How this HOMA-IR calculator works
This HOMA-IR calculator uses the two approximation formulas from the homeostasis model assessment (HOMA) that David Matthews and colleagues in Oxford published in Diabetologia in 1985. Their computer model predicts the fasting glucose and insulin levels that go with each degree of insulin resistance and beta-cell failure, so one fasting pair can be read back as an estimate of both. The paper set the reference so that normal-weight normal subjects under 35 years have an insulin resistance of 1 and a beta-cell function of 100%, and gave the formulas with insulin in µU/mL (the same as mU/L) and glucose in mmol/L. In the paper, normal beta cells follow the line insulin = 5 × (glucose − 3.5); at a glucose of 4.5 mmol/L that gives an insulin of 5 µU/mL, and 5 × 4.5 = 22.5, so that point scores exactly 1.0 and 100%. The paper writes the resistance formula as insulin ÷ (22.5 e−ln glucose), which is the same as insulin × glucose ÷ 22.5.
HOMA-IR = fasting insulin (µU/mL) × fasting glucose (mmol/L) ÷ 22.5
HOMA-IR = fasting insulin (µU/mL) × fasting glucose (mg/dL) ÷ 405
HOMA-%B = 20 × fasting insulin (µU/mL) ÷ (fasting glucose in mmol/L − 3.5)
Glucose: 1 mmol/L = 18 mg/dL, the factor behind 405 (22.5 × 18). Insulin: 1 µU/mL = 6 pmol/L, so pmol/L is divided by 6. HOMA-%B cannot be calculated when glucose is 3.5 mmol/L (63 mg/dL) or less.
The insulin factor matters because two are in use. This calculator divides pmol/L by 6.00, the value Knopp and colleagues set out in 2019 as correct for human insulin; they trace the other common factor, 6.945, to an assumed molar mass of 6000 g/mol and an outdated insulin standard, and note that it under-reports insulin by about 15%. Dividing by 6.945 gives a µU/mL value, and so a HOMA-IR and HOMA-%B, about 14% lower than dividing by 6. If your laboratory reports pmol/L, it can tell you which factor it uses.
What a HOMA-IR result means
A HOMA-IR result has no universal normal range or single cut-off for insulin resistance. The only fixed point in the 1985 paper is the reference value of 1.0 for young, normal-weight adults; a result of 2.0 means the model estimates about twice that degree of insulin resistance. Thresholds published since then come from particular populations, age groups, insulin assays and statistical methods, such as the 75th or 90th percentile of a healthy group, a reference interval, or the value that best predicts metabolic syndrome. In the Spanish EPIRCE study of 2,459 adults, the threshold fell from 3.46 by the 90th percentile to 2.05 when it was set by metabolic syndrome. Insulin assays also differ: Manley and colleagues found results from 11 commercial assays varied by a factor of 2 on the same samples. So a cut-off is only useful from a study of a similar population, ideally measured with a similar assay.
| Study | Population | How the cut-off was set | HOMA-IR value |
|---|---|---|---|
| Yamada 2011 | 2,153 healthy Japanese adults aged 20–79, fasting glucose under 100 mg/dL, BMI under 25 | Reference interval (mean ± 2 SD of log HOMA-IR) | 0.4–2.4; 2.5 or more suggested as insulin resistance |
| Ascaso 2003 | 65 Spanish adults aged 30–60 with normal glucose metabolism | 75th percentile | 2.6 |
| Bonora 1998 (Bruneck) | 225 non-obese Italian adults aged 40–79 with no metabolic disorder | Lower limit of the top quintile | 2.77 |
| Geloneze 2009 (BRAMS) | 297 healthy adults from 1,203 non-diabetic Brazilians aged 18–78 | 90th percentile; metabolic syndrome ROC | Above 2.7; above 2.3 for metabolic syndrome |
| Gayoso-Diz 2013 (EPIRCE) | 2,459 Spanish adults aged 20–92 | 90th percentile; metabolic syndrome ROC | 3.46; 2.05 (1.85 in non-diabetic men) |
| Qu 2011 | 1,854 Mexican American adults in Brownsville, Texas | Machine-learning clustering | 3.80 |
HOMA-%B is read the same way, against 100% as the reference. Wallace and colleagues, from the same Oxford group, list measuring beta-cell function in isolation as an inappropriate use of HOMA: a %B value only makes sense next to the insulin resistance it is compensating for. For why published ranges differ and how the studies were done, see the guide to the HOMA-IR normal range.
HOMA-%B: the beta-cell function estimate
HOMA-%B estimates how much insulin the beta cells are putting out for the fasting glucose, as a percentage of the 100% assigned to young, normal-weight adults in the 1985 model. Matthews and colleagues built the beta-cell part of the model from near-steady-state C-peptide responses to 2.5-hour hyperglycaemic clamps at glucose levels of 7.5, 10 and 15 mmol/L in six normal subjects, whose glucose to C-peptide response was nearly linear with an intercept on the glucose axis of 3.5 mmol/L. That intercept is the 3.5 in the formula, which is why HOMA-%B cannot be calculated at a glucose of 3.5 mmol/L or less. In the paper, HOMA-%B correlated with beta-cell function from the hyperglycaemic clamp (Rs = 0.61) and from an intravenous glucose tolerance test (Rs = 0.64). The authors also found that HOMA assessed beta-cell function less well in normal subjects than in people with diabetes.
Matthews and colleagues noted that the feedback loop raises the basal insulin level to overcome hepatic insulin resistance, so a high HOMA-%B next to a high HOMA-IR reflects that compensation rather than unusually healthy beta cells. Wallace and colleagues reported in 2004 that HOMA had been used about 20 times more often to estimate insulin resistance than beta-cell function.
When HOMA-IR is less reliable
HOMA-IR is an imprecise estimate in one person, and its authors said so. In the 1985 paper the coefficient of variation between repeat estimates was 31% for insulin resistance and 32% for beta-cell function, and the authors wrote that this low precision limits its use. They advised measuring fasting insulin over a 15-minute period in a rested person, because insulin is released in pulses and stress affects it, and noted that sampling three times, 5 minutes apart, improves precision; a single outpatient sample, they wrote, is unlikely to be a reliable guide. Exercise and proinsulin measured as insulin can also affect results. The model was built and tested in people without diabetes and in people with type 2 diabetes treated by diet alone, not in people injecting insulin. Insulin assays add more error: Miller and colleagues found that 7 of 10 commercial methods differed from a mass spectrometry reference by more than 15.5% in 36% to 100% of samples.
HOMA still tracks the reference method well across groups. Matthews found a correlation of 0.88 with the euglycaemic clamp, and Bonora and colleagues found r = −0.820 between HOMA-IR and clamp glucose disposal in 115 people, concluding that HOMA suits large or epidemiological studies with only a fasting sample. The Oxford group later released a computer model, HOMA2, and Levy, Matthews and Hermans wrote in 1998 that correct HOMA evaluation uses the computer program. HOMA2 is a different, updated method and is not built here, and its values are on a different scale: in the Brazilian BRAMS study the 90th-percentile cut-off was 2.7 for the 1985 HOMA-IR and 1.8 for HOMA2-IR.
Questions
What is the HOMA-IR formula?
HOMA-IR = fasting insulin (µU/mL) × fasting glucose (mmol/L) ÷ 22.5, or fasting insulin (µU/mL) × fasting glucose (mg/dL) ÷ 405. For an insulin of 10 µU/mL and a glucose of 90 mg/dL (5.0 mmol/L) it gives 2.22.
What is a normal HOMA-IR?
There is no single normal value. The 1985 model sets 1.0 as the reference for young, normal-weight adults, and published cut-offs for insulin resistance range from 1.85 to 3.80 in the adult studies listed above, depending on the population, the assay and the method. A Japanese reference interval study found 0.4 to 2.4 in healthy adults.
How do I convert insulin from pmol/L to µU/mL?
This calculator divides pmol/L by 6, so 60 pmol/L is 10 µU/mL. Some laboratories and references use 6.945, which gives a value about 14% lower. Knopp and colleagues argue that 6.00 is the correct factor for human insulin.
Is HOMA-IR the same as HOMA2-IR?
No. HOMA2 is the updated Oxford computer model and gives different numbers from the 1985 formulas used here, so cut-offs for one do not apply to the other.
Is my data sent anywhere?
No. The calculation runs in your browser, and the values you enter are not sent or stored.
Sources
- Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC. Homeostasis model assessment: insulin resistance and β-cell function from fasting plasma glucose and insulin concentrations in man. Diabetologia. 1985;28(7):412–419. doi:10.1007/BF00280883
- Wallace TM, Levy JC, Matthews DR. Use and abuse of HOMA modeling. Diabetes Care. 2004;27(6):1487–1495. doi:10.2337/diacare.27.6.1487
- Levy JC, Matthews DR, Hermans MP. Correct homeostasis model assessment (HOMA) evaluation uses the computer program. Diabetes Care. 1998;21(12):2191–2192. doi:10.2337/diacare.21.12.2191
- Knopp JL, Holder-Pearson L, Chase JG. Insulin units and conversion factors: a story of truth, boots, and faster half-truths. J Diabetes Sci Technol. 2019;13(3):597–600. doi:10.1177/1932296818805074
- Bonora E, Targher G, Alberiche M, et al. Homeostasis model assessment closely mirrors the glucose clamp technique in the assessment of insulin sensitivity. Diabetes Care. 2000;23(1):57–63. doi:10.2337/diacare.23.1.57
- Manley SE, Stratton IM, Clark PM, Luzio SD. Comparison of 11 human insulin assays: implications for clinical investigation and research. Clin Chem. 2007;53(5):922–932. doi:10.1373/clinchem.2006.077784
- Miller WG, Thienpont LM, Van Uytfanghe K, et al. Toward standardization of insulin immunoassays. Clin Chem. 2009;55(5):1011–1018. doi:10.1373/clinchem.2008.118380
- Yamada C, Mitsuhashi T, Hiratsuka N, et al. Optimal reference interval for homeostasis model assessment of insulin resistance in a Japanese population. J Diabetes Investig. 2011;2(5):373–376. doi:10.1111/j.2040-1124.2011.00113.x
- Ascaso JF, Pardo S, Real JT, et al. Diagnosing insulin resistance by simple quantitative methods in subjects with normal glucose metabolism. Diabetes Care. 2003;26(12):3320–3325. doi:10.2337/diacare.26.12.3320
- Bonora E, Kiechl S, Willeit J, et al. Prevalence of insulin resistance in metabolic disorders: the Bruneck Study. Diabetes. 1998;47(10):1643–1649. doi:10.2337/diabetes.47.10.1643
- Geloneze B, Vasques AC, Stabe CF, et al. HOMA1-IR and HOMA2-IR indexes in identifying insulin resistance and metabolic syndrome: Brazilian Metabolic Syndrome Study (BRAMS). Arq Bras Endocrinol Metabol. 2009;53(2):281–287. doi:10.1590/S0004-27302009000200020
- Gayoso-Diz P, Otero-González A, Rodriguez-Alvarez MX, et al. Insulin resistance (HOMA-IR) cut-off values and the metabolic syndrome in a general adult population: effect of gender and age: EPIRCE cross-sectional study. BMC Endocr Disord. 2013;13:47. doi:10.1186/1472-6823-13-47
- Qu HQ, Li Q, Rentfro AR, Fisher-Hoch SP, McCormick JB. The definition of insulin resistance using HOMA-IR for Americans of Mexican descent using machine learning. PLoS One. 2011;6(6):e21041. doi:10.1371/journal.pone.0021041