In one sentence An infusion pump is programmed in millilitres per hour, and that number is the volume the patient receives in each hour.
An infusion pump is set in millilitres per hour
An infusion pump is a machine that pushes fluid into a vein at a speed the nurse chooses and then holds constant. Because the speed is constant, the fluid does not run faster when the bag is full or slower when it is nearly empty, the way a gravity drip does. The number the nurse types in is a rate, measured in millilitres per hour and written mL/hr. Read it as “millilitres per hour”: mL means millilitre, the unit of volume, and hr means hour, the unit of time. A setting of 125 mL/hr means that after one hour 125 mL have entered the patient, after two hours 250 mL, and after eight hours 1,000 mL. That is why the two quantities the nurse takes from the order are the total volume in millilitres and the total time in hours: everything else is worked out from those two.
An order reads 500 mL of sodium chloride 0.9 % over 4 hours. The nurse programmes 125 mL/hr, which means 125 mL in each of the four hours.
A pump is set at 90 mL/hr. How much fluid has been delivered after 3 hours, and what single multiplication gives it?
Show the answer
The rate is the amount for one hour, so three hours deliver 90 × 3 = 270 mL. Multiplying the rate by the number of hours is the quickest way to predict the total.
Read detailed explanations
- Time is counted in sixties, not in hundreds
The reason a time of six hours thirty minutes cannot be written 6.30 is historical and structural: the hour is a sexagesimal unit, inherited from Babylonian astronomy, divided into sixty minutes, and each minute again into sixty seconds. Decimal notation, by contrast, groups digits in tens. Whenever two counting systems meet inside one calculation, one of them must be converted before the arithmetic can proceed, and here the decimal system wins, because the pump rate is a decimal quantity. That conversion has a direction, and the reverse direction is used just as often. Going from minutes to decimal hours, divide the minutes by sixty: thirty minutes become 0.5 hours. Going back, multiply the decimal part by sixty: 0.25 hours becomes fifteen minutes. The two moves are inverses, so they cancel. The most common clinical version of the mistake is the phantom decimal: a nurse reads six hours twenty minutes as 6.20 hours and divides a volume by it, when the correct value is 6.333 hours. Because 6.20 is smaller than 6.333, the divisor is too small and the computed rate comes out too high. Direction matters in both cases: when the minutes are converted downward, the pump is set too fast; when the true decimal is smaller than the value used, the pump is set too slow. Reading the answer back into minutes is the habit that catches it.
- One invariant behind both directions
The two formulas are not two rules to be memorised but one equation seen from two sides, and naming that equation makes both directions obvious. The invariant is that the volume delivered equals the rate multiplied by the infusion time, written V = r × t; both working formulas are rearrangements of that one sentence. Because a pump holds r constant, the volume grows in direct proportion to the time, so a graph of volume against time is a straight line through the origin whose slope is the rate (beyond the supplied notes: this uses the straight-line graphs you will meet in section 4.4; for now, read the slope as the rate in mL/hr). This is what makes the multiply-back check meaningful rather than circular: it tests whether the three quantities satisfy the same proportionality, and it also predicts later behaviour. If a pump has been running for two hours at 80 mL/hr, then 160 mL should have left the bag; if the bag shows 300 mL gone, the discrepancy points to a priming volume, a second infusion piggybacked on the same line, a pump fault, or an infiltration, and it should be investigated before more fluid is given. The relationship also tells you what happens when an order changes: doubling the volume at the same rate doubles the duration, while doubling the rate at the same volume halves it. Reasoning about these proportional changes is faster and safer than recomputing from scratch, and it is how an experienced nurse notices immediately that an order of 1,000 mL in 4 hours is implausibly fast while the same volume in 24 hours is implausibly slow.
- Checking the setting, and the arithmetic of rounding
A calculated rate is a proposal, not yet a setting. Before the pump is started, the nurse compares three things: the rate, the volume to be infused, and the time written on the order, then asks whether the three agree. The multiply-back test is the arithmetic version of that comparison, and it must be done with the decimal hours actually used, not with a remembered approximation. Rounding deserves its own rule, because its error is silent and cumulative. Let the exact rate be R and the programmed rate be P. After t hours the difference in delivered volume is (P − R) × t. A rounding of half a millilitre per hour therefore becomes 4 mL after eight hours and 12 mL after a day, which is why a policy that is harmless for maintenance saline can be unacceptable for a concentrated electrolyte or a vasoactive drug. Three practical rules follow. First, enter as many decimal places as the pump allows before rounding. Second, round in the direction the policy prescribes for that class of infusion, and record the setting together with the reason. Third, recheck the infusion at handover and whenever the bag is replaced, because pumps drift, lines kink, cannulae infiltrate tissue, and the volume remaining is the only independent evidence of what has actually been delivered. The pump’s own history and the graduations on the bag are the audit trail; the calculation only tells you what should have happened.