Repeatability and reproducibility limits: where 2.77 comes from

Updated: September 30, 2026 · ISKRIT

Two results on the same sample never agree exactly. The repeatability limit is the largest difference you may accept before deciding something went wrong, and it is a fixed multiple of the method's standard deviation.

Calculator

Two standard deviations from the method or from your own data.

The formula and the factor

r = 2.77 · sr and R = 2.77 · sR

where sr is the repeatability standard deviation and sR the reproducibility one. The factor is not arbitrary. The difference of two independent results has a standard deviation of √2 times the standard deviation of one result, and a 95 % two-sided interval is 1.96 standard deviations wide, so the multiplier is 1.96 · √2 = 2.77.

The two sets of conditions

Repeatability conditions mean the same method, the same laboratory, the same operator, the same equipment and a short interval of time. Reproducibility conditions mean the same method on the same material in different laboratories, with different operators and equipment. Everything between those two, same laboratory but a different day or a different analyst, is intermediate precision, and using r where intermediate precision applies is the most common misuse of the limit.

Using it

Duplicate determinations giving 12.4 and 13.1 mg/l, on a method with sr = 0.28 mg/l, are compared against r = 2.77 · 0.28 = 0.78 mg/l. The difference of 0.7 is inside the limit, so the pair is accepted and the result reported as their mean. Had the difference been 0.9, the standard response is to repeat the determination, not to average anyway and not to discard the inconvenient one.

Where the standard deviations come from

They are properties of the method, established in a collaborative study or taken from the method's own precision statement, not computed from the two results being compared. A laboratory that estimates sr from the very pair it is testing has built a circular check that can never fail. Internal quality control data accumulated over months is the legitimate in-house source, and it should be revalidated when equipment or reagents change.

Questions

Where does the factor 2.77 come from? The difference of two independent results has a standard deviation √2 times that of one result, and a 95 percent two-sided interval is 1.96 standard deviations wide, so the factor is 1.96 · √2 = 2.77.

What is the difference between repeatability and reproducibility conditions? Repeatability means the same method, laboratory, operator and equipment within a short time. Reproducibility means the same method on the same material in different laboratories. Anything in between is intermediate precision, and r does not apply to it.

Repeatability and reproducibility limits, and the comparison of a result pair against them, are handled in the internal quality control tool.