The relative fat mass calculator above implements one specific published equation. RFM equals 64 minus 20 times height divided by waist circumference, plus 12 times a sex term that is 0 for men and 1 for women. Two measurements, one line of arithmetic, and no weight required — which is what makes it different from almost every other body fat estimate.
Arb Digital publishes this because the equation is genuinely useful and its limits are genuinely large, and both facts deserve equal space. It was developed on a large national survey dataset and validated against DXA scanning, and the paper reports its own performance in numbers rather than adjectives. Those numbers are reproduced below, honestly, because an estimate whose error you cannot see is worse than no estimate at all.
What This Relative Fat Mass Calculator Does
It computes the published RFM value from height, waist and the sex term, and shows the height-to-waist ratio the equation is built on. If you enter a weight it converts the percentage into fat mass and fat-free mass in kilograms, which is a straightforward multiplication and not part of the model.
It does not classify, band, score or judge. The source paper used RFM in the context of body fat-defined obesity thresholds for population research, and applying those thresholds to an individual on a web page would be a clinical act this page has no standing to perform. The number is reported and left as a number.
This complements rather than replaces the other body composition tools on the site. Our body fat calculator implements the Navy circumference method, which needs neck and hip measurements in addition to height and waist. The skinfold body fat calculator uses caliper measurements. The lean body mass calculator estimates lean mass from published formulas based on height and weight rather than from a fat percentage. Different inputs, different equations, and answers that will not match.
How to Use It
- Measure waist properly. This is the whole calculation. A tape held at the wrong height or pulled tight moves the answer by several percentage points.
- Keep both measurements in the same unit. The equation uses a ratio, so centimetres and inches both work — but mixing them produces nonsense.
- Set the sex term. The published model uses 0 and 1, and the effect is a flat 12 percentage point difference between the two constants.
- Add weight only if you want kilograms. It converts the percentage into mass and has no effect on the RFM figure itself.
- Read the accuracy section before acting on the number. The paper's own accuracy criterion is much looser than the two decimal places a calculator can print.
The Equation and Where It Comes From
The equation was published as Relative fat mass (RFM) as a new estimator of whole-body fat percentage — A cross-sectional study in American adult individuals in Scientific Reports in 2018. The authors generated 365 candidate anthropometric indices and selected the final form: 64 − (20 × height / waist circumference) + (12 × sex), with sex = 0 for men and 1 for women.
The study population is named precisely in the paper. Development used National Health and Nutrition Examination Survey data from 1999 to 2004 (n = 12,581), and validation used NHANES 2005 to 2006 data (n = 3,456), in adults aged 20 and over, with whole-body fat percentage measured by dual energy X-ray absorptiometry as the reference. Mean DXA-measured fat percentage in those datasets was around 39 to 40 percent in women and 28 percent in men.
Worth noting: the paper explicitly tested height/waist against the more familiar waist/height ratio and found height/waist predicted body fat percentage better with a lower root mean squared error, which is why the equation is written the way it is. Adding age or ethnicity to the model did not improve the coefficient of determination, so neither appears in the final form.
Worked Example
A man with a height of 175 cm and a waist of 90 cm. Height divided by waist is 175 ÷ 90 = 1.944. Twenty times that is 38.89. RFM is 64 − 38.89 + 0 = 25.1 percent. At a body weight of 80 kg, that is 20.1 kg of fat mass and 59.9 kg of fat-free mass.
The same measurements with the sex term set to 1 give 76 − 38.89 = 37.1 percent, because the constant becomes 64 + 12. And in inches the arithmetic is identical: 68.9 inches divided by 35.4 inches is still 1.944. That unit independence is a genuine convenience of a ratio-based equation and a good way to check you entered the numbers correctly.
How Accurate Is It, in the Paper's Own Numbers
In the validation dataset, RFM explained 69 percent of the variation in DXA-measured body fat percentage among women and 75 percent among men, compared with 65 and 61 percent for BMI. Median bias was small: 0.9 percent among women and 0.5 percent among men. So on average, across a large sample, RFM lands close.
The accuracy figure needs reading carefully, because it is where most reporting of this equation goes wrong. The paper defines accuracy as the proportion of estimates falling within 20 percent of the DXA-measured value — a proportional band, not a fixed one. RFM met that criterion for 91.5 percent of women, against 21.6 percent for BMI, which is a large and real improvement. But at a true value of 30 percent body fat, being "within 20 percent" means anywhere from 24 to 36 percent. That is a six percentage point spread on either side, in an equation that met its own accuracy test.
The practical reading is: RFM is good at telling large differences apart and poor at telling small ones apart. A change from 25 to 33 percent means something. A change from 25.1 to 25.6 percent means nothing at all, and the decimal place the calculator prints is a display convention rather than a claim. The paper also lists its own limitations, including that DXA itself underestimates fat percentage in the lower ranges and in men and overestimates it in the higher ranges and in women relative to the four-compartment method.
Waist Measurement Is the Whole Game
Because the equation has exactly one variable input, everything rests on measuring waist consistently. The StatPearls review Anthropometric Measurement covers standard technique for circumference measures. Different protocols specify different landmarks — at the narrowest point, at the navel, or at the midpoint between the lowest rib and the iliac crest — and they do not give the same number on the same person.
The arithmetic makes the stakes plain. At 175 cm height, a waist of 90 cm gives 25.1 percent and a waist of 95 cm gives 27.2 percent. Five centimetres of tape placement is two percentage points of estimated body fat. Breathing state, tape tension, clothing and time of day all move the reading, and none of that is biology.
If you are tracking a change over time, the fix is protocol rather than precision: same landmark, same tape, same time of day, same breathing state, ideally the same person measuring. Our waist-to-height ratio calculator and waist-to-hip ratio calculator use the same measurement and inherit exactly the same sensitivity, and the BMI calculator avoids it entirely by not using waist at all.
Arb Digital builds calculators and content that cite their sources and state their error ranges plainly — the same standard as this page.
Browse All Free Tools Talk To Our TeamCommon Mistakes to Avoid
- Mixing units between height and waist — the ratio only works if both use the same unit, and mixing them produces a meaningless number.
- Reading the decimal place as meaningful — the paper's accuracy criterion is within 20 percent of the DXA value, which is several percentage points wide at typical readings.
- Changing waist landmark between measurements — five centimetres of tape placement is about two percentage points of estimated fat at average height.
- Comparing RFM with a different method's answer — Navy circumference, skinfolds and RFM use different equations and different inputs, and they are not expected to agree.
- Applying it outside the study population — the equation was developed and validated in American adults aged 20 and over, and was not built for children or adolescents.
Related Free Tools From Arb Digital
Estimate body fat by the Navy circumference method with the body fat calculator, use calipers with the skinfold body fat calculator, estimate lean mass with the lean body mass calculator, compute BMI with the BMI calculator, or work with waist ratios in the waist-to-height ratio calculator and the waist-to-hip ratio calculator. The full free online tools hub lists every health tool we publish.
Frequently Asked Questions
RFM equals 64 minus 20 times height divided by waist circumference, plus 12 times a sex term that is 0 for men and 1 for women. It was published in Scientific Reports in 2018 and uses only two measurements.
American adults aged 20 and over in the National Health and Nutrition Examination Survey: 1999 to 2004 data for development, with 12,581 participants, and 2005 to 2006 data for validation, with 3,456 participants, using DXA as the reference method.
In validation it explained 69 percent of the variation in DXA-measured fat percentage among women and 75 percent among men, with median bias of 0.9 and 0.5 percent. Its accuracy criterion is estimates falling within 20 percent of the DXA value, which is a wide band at typical readings.
Yes, as long as both height and waist use the same unit. The equation depends on the ratio of the two, which is unitless, so the answer is identical either way.
The authors tested both and found height/waist predicted body fat percentage better, with a lower root mean squared error, across sexes, ethnic groups and age categories. That is why waist/height was dropped from the final model.
The authors tested it. Adding age did not improve the coefficient of determination for either women or men, and neither did ethnicity, so neither variable appears in the final published form.
They are different equations with different inputs. The Navy circumference method needs neck and hip measurements as well, so the two will not agree, and neither result should be treated as a correction of the other.
No. It reports the value the published equation produces and nothing else. It sets no target, applies no category, and makes no judgement. Body composition questions belong with a doctor or a registered dietitian.
This page implements a published estimating equation for general information only. It is not medical advice, it applies no health category and sets no target for anyone, and it is not a substitute for advice from a qualified doctor or registered dietitian.
