Pipette Calibration Gravimetric Calculator
Pipette Calibration Gravimetric Calculator
Convert a weighed mass of water into a delivered volume with the ISO 8655 Z factor, and read off the systematic error against the pipette’s nominal volume.
Systematic error
Mass × Z vs nominal → % errorA 100 µL pipette set to 100 µL, ten deliveries of water at 22 °C averaging 99.1 mg, Z = 1.0033 µL/mg
Formula
systematic error (%) = (V̄ − Vnominal) ÷ Vnominal × 100
random error, CV (%) = s ÷ V̄ × 100
- m
- net mass of water delivered, in milligrams
- Z
- the conversion factor from mass of water to volume in µL/mg, at the water’s temperature and the ambient pressure. It folds together the density of water and the buoyancy of the air the balance is weighing in
- V̄
- the mean of the replicate volumes at one setting — ten of them, under ISO 8655
- systematic error
- also called inaccuracy or bias. A signed quantity: negative means the pipette under-delivers
- s
- the sample standard deviation of the replicate volumes, which becomes the random error or imprecision when expressed as a coefficient of variation
Worked example
A 100 µL pipette set to 100 µL, ten deliveries of water at 22 °C averaging 99.1 mg, Z = 1.0033 µL/mg
V̄ = 99.1 × 1.0033 = 99.427 µL
(99.427 − 100) ÷ 100 × 100 = −0.57%
The pipette delivers about 0.57 µL less than it is set to
Ignore Z and you would report 99.1 µL and a −0.90% error — the buoyancy and density correction is a third of the apparent bias here
For the random error, take the standard deviation of the same ten weighings: an SD of 0.194 mg is 0.195 µL, a CV of 0.20%
Z factor for distilled water at 101.3 kPa (ISO 8655)
| Water temperature | Z (µL/mg) | Effect on a 100 µL delivery |
|---|---|---|
| 20 °C | 1.0029 | +0.29 µL over the raw mass |
| 21 °C | 1.0031 | +0.31 µL |
| 22 °C | 1.0033 | +0.33 µL |
| 23 °C | 1.0035 | +0.35 µL |
| 24 °C | 1.0038 | +0.38 µL |
| 25 °C | 1.0040 | +0.40 µL |
What ISO 8655 asks for
| Requirement | Value |
|---|---|
| Test volumes | Three: the nominal volume, 50% of nominal, and the greater of 10% of nominal or the lowest settable volume |
| Replicates | At least 10 measurements at each volume for calibration; at least 4 for routine in-house checks |
| Ambient temperature | (20 ± 3) °C, varying by no more than 0.5 K during the test |
| Water temperature | Within 0.5 K of the ambient air temperature |
| Relative humidity | 45% to 80% |
| Air movement | Draught free |
| Balance resolution | 0.001 mg for 0.5–20 µL, 0.01 mg for 20–200 µL, 0.1 mg for 200 µL–10 mL |
A ten-replicate run, written out
| Replicate | Mass (mg) | Volume at Z = 1.0033 (µL) |
|---|---|---|
| 1–10 masses | 99.4, 98.9, 99.2, 99.0, 99.3, 98.8, 99.1, 99.2, 98.9, 99.2 | — |
| Mean | 99.10 | 99.427 |
| Standard deviation | 0.194 | 0.195 |
| Systematic error | — | −0.57% of nominal |
| Random error (CV) | — | 0.20% |
What makes the number mean something
Gravimetric verification is the reference method because mass is the quantity a laboratory can measure best. Deliver water onto a balance, weigh it, and convert the mass to a volume. The conversion is the Z factor, which is not merely the reciprocal of water’s density: it also corrects for the buoyancy of the air the balance is weighing in, since a vessel of water displaces air and therefore weighs slightly less than its true mass. At 22 °C and 101.3 kPa, Z is 1.0033 µL/mg. Across the whole 20–25 °C range it moves by about 0.11%, so a degree or two of uncertainty in the water temperature is not what makes a calibration fail. Leaving Z out altogether, and treating a milligram as a microlitre, is a 0.3% error — a third of a typical tolerance, applied in the same direction every time.
Two numbers come out of one set of weighings and they answer different questions. The systematic error is the mean delivered volume minus the volume the pipette was set to, as a percentage of that setting: it says whether the instrument is delivering the right amount on average, and it is usually correctable by adjustment. The random error is the coefficient of variation of the replicates: it says whether it delivers the same amount twice, and no adjustment will improve it. A pipette with a 2% bias and a 0.2% CV needs recalibrating. A pipette with no bias and a 2% CV needs a service, or its operator needs retraining, because a leaking seal, a worn piston, an inconsistent plunger stop or a variable pre-wet all show up in the scatter and not in the mean.
ISO 8655 asks for ten measurements at each of three volumes: the nominal volume, half of it, and the greater of a tenth of it or the lowest the pipette can be set to. The three-point requirement is what makes the test worth doing, because the error at the bottom of the range is set by different parts of the mechanism than the error at the top, and a pipette that is perfect at 1,000 µL can be 10% out at 100 µL. An in-house check that tests only the nominal volume will not find that.
Three practical things decide whether the result means anything at all. Evaporation is the first: microlitres of water on a balance pan disappear at a rate that is negligible against 1,000 µL and dominant against 2 µL, and the answer is a weighing vessel with a narrow neck, an evaporation trap or a moistened chamber, and a consistent short interval between dispensing and reading — or an explicit evaporation correction measured by watching the drift with nothing being added. Balance resolution is the second: ISO 8655 requires 0.001 mg for volumes below 20 µL, because at 1 µL a 0.01 mg readability is already 1% of the measurement, and no amount of replication rescues a reading the balance cannot resolve. Thermal equilibration is the third, and it is the one that gets skipped: the standard requires the water to be within 0.5 K of the ambient air, the room to be 20 ± 3 °C and to vary by no more than 0.5 K during the test, and the whole thing to be done out of a draught. Water taken from a cold tap is not at room temperature, and the pipette itself, warmed by a hand, expands the air in its shaft and pushes out more liquid than intended.
The last step is the one this calculator will not do for you: deciding whether the number passes. There is no universal tolerance. ISO 8655-2 sets maximum permissible errors, and the 2022 revision changed how — tolerances are now expressed as a proportion of the pipette’s nominal volume, so a 300 µL air-displacement pipette carries the same ±2.4 µL limit at 30, 150 and 300 µL rather than a proportionally looser one at the bottom of the range. That makes the 10% test point much harder to pass than it was under the older edition, and it is the right way round: an absolute error is an absolute error whatever the setting. The applicable figure for any given pipette has to come from the standard itself or from the manufacturer’s data sheet, and a laboratory may set a tighter limit than either if the application demands it. What it should not do is compare the result against a number someone remembered.
Frequently asked questions
What is the Z factor and why do I need it?
It converts a weighed mass of water into a volume, correcting both for water’s density at the measurement temperature and for the buoyancy of the air the balance weighs in. At 22 °C and 101.3 kPa it is 1.0033 µL/mg. Treating milligrams as microlitres understates the volume by about 0.3%.
How many measurements does ISO 8655 require?
At least ten at each of three volumes — the nominal volume, 50% of nominal, and the greater of 10% of nominal or the lowest settable volume. Routine in-house checks may use four per volume, but a calibration uses ten.
What is the difference between systematic and random error?
Systematic error is the mean delivered volume against the set volume, expressed as a percentage: it measures accuracy and can usually be adjusted out. Random error is the coefficient of variation of the replicates: it measures precision, and a poor CV points at a seal, a piston or the technique, not at the calibration.
What tolerance should I compare the result against?
The maximum permissible error in ISO 8655-2 for that type and volume, or the manufacturer’s data sheet, whichever your quality system specifies. There is no single universal figure, which is why this calculator reports the error and does not grade it.
Why does ISO 8655 test at 10% of nominal volume?
Because that is where pipettes fail. The error at the bottom of the range is governed by different parts of the mechanism than the error at the top, and the 2022 revision made the point sharper by setting the tolerance as a fixed proportion of nominal volume, so the same absolute limit applies at 10% as at 100%.
How do I stop evaporation ruining a small-volume calibration?
Use a weighing vessel with a narrow neck or an evaporation trap, keep the interval between dispensing and reading short and consistent, and if you cannot eliminate it, measure the drift with nothing being dispensed and apply it as a correction. At a few microlitres, evaporation is easily larger than the tolerance.
Does the water temperature need to match the room?
Yes — within 0.5 K, and the room itself must be 20 ± 3 °C and stable to within 0.5 K during the test. Water straight from a tap is not at room temperature, and the mismatch changes both the density and the air inside the pipette shaft.
Related calculators
References
- International Organization for Standardization. ISO 8655: Piston-operated volumetric apparatus — Part 2 (pipettes, maximum permissible errors) and Part 6 (gravimetric reference method, Z factors, test volumes and replication).
- Sartorius. Pipette Calibration and Compliance: A Practical Guide to ISO 8655 — the 2022 revision’s proportional tolerances, the environmental requirements, the balance resolution table and the systematic and random error formulas.
- Cal Lab: The International Journal of Metrology, Jan–Mar 2018. Calibrating a Micropipette — ISO 8655-6’s three test volumes and ten repeat measurements at each.
- Eppendorf. SOP — factor Z for distilled water — the Z factor overview table in µL/mg in accordance with EN ISO 8655.
- Acta IMEKO 2021;10(3). Uncertainty of factor Z in the gravimetric volume determination — the derivation of Z from water density, air density and the density of the reference weights.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.