Why a pump rate is never the same as a dose
A pump meters volume. A prescriber orders drug. The bridge between them is the concentration of the bag, and every infusion error that is not an arithmetic slip is a mismatch between the bag someone hung and the concentration someone else assumed.
The order says 1,000 units/hour of heparin. The pump cannot accept that; it wants millilitres per hour. If the bag holds 25,000 units in 250 mL, each millilitre carries 100 units, so 1,000 units per hour is 10 mL per hour. Hang the same order on a bag of 25,000 units in 500 mL and the correct rate doubles to 20 mL/hour — same drug, same order, same patient, twice the volume on the pump.
That is why standardised concentrations matter more than arithmetic skill. ISMP publishes standard concentration lists for adult and neonatal infusions so that a unit stocks one strength of each high-alert drug rather than three, and so that the rate a nurse expects to see is the rate that appears. This calculator gives you the number for whatever bag you actually have in front of you, and the reverse check tells you what dose a running pump is currently delivering — which is the question you need answered when you take over a patient mid-infusion.
The formula, read as a unit cancellation
Start with the concentration. Divide the amount of drug in the bag by the final volume of the bag, and you have amount per millilitre. Note the word final: adding 10 mL of drug to a 250 mL bag makes 260 mL, and if your practice is to add drug without removing an equal volume, the true concentration is lower than the label arithmetic suggests. For most infusions the difference is small; for concentrated additives it is not.
Then divide the dose per hour by that concentration. Units per hour divided by units per millilitre leaves millilitres per hour, and the drug unit — units, milligrams, micrograms, millimoles — cancels out entirely. This is why the calculator does not care which unit you use, provided the bag and the order use the same one. Mixing milligrams in the bag with micrograms in the order produces an answer a thousand times wrong, and nothing in the arithmetic will complain.
A per-kilogram order needs one multiplication first. 0.5 mg/kg/hour at 70 kg is 35 mg/hour, and 35 mg/hour on a 4 mg/mL bag is 8.75 mL/hour. If the order is written per kilogram per minute rather than per hour — as vasopressor and inotrope orders usually are — use the mcg/kg/min to mL/hr calculator, which folds in the factor of 60.
Two by-products fall out of the same numbers. Bag volume divided by rate is the run time, which tells you when to have the next bag ready. Rate multiplied by 24 is the daily volume, which belongs on the fluid balance chart and matters a great deal in heart failure and renal impairment, where the diluent can be a bigger clinical problem than the drug.
Worked example: heparin 25,000 units in 250 mL at 1,000 units/hour
A patient is started on a heparin infusion. The pharmacy supplies 25,000 units in 250 mL of dextrose. The order is 1,000 units/hour.
- Concentration. 25,000 units ÷ 250 mL = 100 units/mL.
- Dose per hour. 1,000 units/hour, taken straight from the order.
- Pump rate. 1,000 ÷ 100 = 10 mL/hour.
- Run time. 250 mL ÷ 10 mL/h = 25 hours.
- Daily volume. 10 × 24 = 240 mL in 24 hours.
Six hours later the anti-Xa result comes back low and the protocol calls for an increase to 1,200 units/hour. Because the concentration is fixed, you can scale directly: 1,200 ÷ 100 = 12 mL/hour. Equivalently, the dose rose by 20% so the rate rises by 20%, from 10 to 12. That proportionality is what makes the titration table in the results panel usable at the bedside.
Now the reverse question, which is the one you face on handover. The pump reads 14 mL/hour and you want to know the dose. Multiply by the concentration: 14 × 100 = 1,400 units/hour. If the chart says 1,000 units/hour, either the rate was changed without documentation or the bag hanging is not the bag the chart assumes — and the second possibility is the dangerous one. Check the bag label before you touch the pump.
How to sanity-check the rate you get
Look at the magnitude first. Most continuous infusions on a general ward run somewhere between 1 and 50 mL/hour, and most intermittent antibiotic infusions run at 50 to 250 mL/hour for a defined period. A continuous infusion computing at 400 mL/hour is telling you the bag is too dilute for the dose, and one computing at 0.3 mL/hour is telling you it is too concentrated; both are correct arithmetic and poor bag design.
Very low rates deserve particular suspicion. Below about 0.5 mL/hour, the drug takes a long time to traverse the dead space of the line, occlusions take a long time to raise pressure and alarm, and small mechanical variations become a large fraction of the delivered dose. Neonatal and paediatric practice manages this with deliberately dilute standard concentrations and short, small-bore lines rather than by accepting a very low rate.
Check the run time against your workflow. A bag that lasts 3 hours will need replacing during the night; a bag that lasts 40 hours may exceed the hang-time limit your policy sets for that drug and diluent. And check the 24-hour volume against the patient's fluid allowance — for a fluid-restricted patient, a diluent volume that arrives quietly through three separate infusions is a common and avoidable cause of overload.
Common infusion concentrations and the rate for a typical order
| Bag | Concentration | Example order | Pump rate |
|---|---|---|---|
| 25,000 units / 250 mL | 100 units/mL | 1,000 units/h | 10 mL/h |
| 25,000 units / 500 mL | 50 units/mL | 1,000 units/h | 20 mL/h |
| 100 units / 100 mL | 1 unit/mL | 4 units/h | 4 mL/h |
| 1,000 mg / 250 mL | 4 mg/mL | 100 mg/h | 25 mL/h |
| 2,000 mg / 500 mL | 4 mg/mL | 200 mg/h | 50 mL/h |
| 500 mg / 100 mL | 5 mg/mL | 250 mg over 1 h | 50 mL/h |
| 40 mmol / 1,000 mL | 0.04 mmol/mL | 10 mmol/h | 250 mL/h |
Rows two and one are the same drug and the same order at two different bag volumes, and the correct rates differ by a factor of two. Rows four and five share a concentration, so the rate scales exactly with the dose.
Where infusion rate errors come from
- Assuming the concentration. The same drug is supplied at several strengths. Read the bag you are hanging, every time.
- Mixing units between the bag and the order. Milligrams in the bag and micrograms in the order is a thousand-fold error that computes cleanly.
- Using the diluent volume instead of the final volume. Adding drug without withdrawing an equal volume raises the total and lowers the true concentration.
- Forgetting the weight in a per-kilogram order. Entering 0.5 mg/h when the order says 0.5 mg/kg/h under-doses an 80 kg adult eighty-fold.
- Programming the dose into a pump expecting volume. A pump in mL/hour mode accepts 1,000 without complaint when 10 was meant.
- Ignoring the carrier fluid. The diluent counts toward the daily fluid balance, and for several infusions it dominates it.
- Not re-checking after a bag change. A new bag from a different supplier can carry a different concentration at the same nominal dose.
What this calculation assumes
It assumes the bag contains exactly the amount stated, in exactly the volume stated, and that the pump delivers what it is programmed to. Volumetric pumps are typically accurate to within a few percent under laboratory conditions, and less so with viscous fluids, long lines, high back-pressure or a partly occluded cannula. For drugs where that matters — insulin, vasopressors, chemotherapy — the clinical response and the monitoring, not the pump display, tell you what the patient is receiving.
It assumes a continuous infusion at a fixed rate, with no bolus, no line flush and no interruption. Bolus doses given from the same bag are not subtracted from the run time, and the line's priming volume — roughly 15 to 25 mL for a standard set — is not accounted for, which means the first drug reaches the patient later than the pump start time suggests at low rates.
It does not check compatibility, stability or hang time. Whether the drug is stable in that diluent, for that long, at that concentration, in that light, is a pharmacy question, and no arithmetic answers it. Nor does it validate the dose: for a weight-based order, confirm the milligrams first with the weight-based dosage calculator, and for a body-surface-area order with the BSA calculator.
High-alert infusions need an independent double check
Heparin, insulin, opioids, vasopressors, concentrated electrolytes and chemotherapy appear on every high-alert medication list, and every one of them is normally given by infusion. Local policy for these drugs almost always requires a second qualified person to verify the drug, the concentration, the dose, the rate and the pump programming independently — meaning the second person calculates the rate themselves rather than confirming yours. Smart-pump dose-error reduction software adds a further layer, but only for drugs that have been entered into the library, and only when the drug is selected from it.
Choosing the right rate calculation
Three different orders lead to three different calculations, and picking the wrong one is a silent error. If the order gives an amount per hour, or per kilogram per hour, this calculator is the right tool. If the order gives an amount per kilogram per minute — the standard form for noradrenaline, dopamine, dobutamine and most sedatives — use the mcg/kg/min converter, which multiplies by 60 before dividing by the concentration. If the order gives a volume over a time with no drug rate at all, the rate is simply volume ÷ hours, and on a gravity set you convert that to drops with the drip rate calculator.
For fluid resuscitation the volume comes first and the rate second: the Parkland formula calculator produces both halves of a burn resuscitation and the hourly rate for each. And when the drug arrives as a powder, the concentration you feed into any of these depends on the diluent volume you add, which is what the reconstitution calculator resolves.