Up next
IV Volume, Time & Rate Basics
Understand volume, time and rate as three connected values within one constant-rate interval before choosing a calculation.
MedMaths Learn pathway
IV Calculations
Learn rates, durations, drops, pump calculations and infusion relationships in a clear step-by-step progression.
8 lessonsabout 2 hoursProgress saved in this browser
Continue learning
IV Volume, Time & Rate Basics
Pick up where you left off, or start with the next lesson in this topic.
Topic pathway
Work through IV Calculations
Follow the order below for a structured pathway, or open any lesson when you need that skill.
Not started
IV Pump Rate (mL/hr)
Calculate mL/hr from a verified volume and time, including times stated in minutes.
Not started
Infusion Time & Finish Time
Calculate duration from remaining volume and mL/hr, then interpret decimal hours safely.
Not started
Drops per Minute (gtt/min)
Use the giving-set drop factor, volume and time in minutes to calculate a gravity drip rate.
Not started
Calculated Medication Amount Over Time
Use concentration and a stated or calculated infused volume to calculate a medication amount for one verified infusion interval.
Not started
Medication Rate (mg/hr & mg/min)
Calculate the medication dose rate represented by a verified concentration and matching current mL/hr, then convert mg/hr ↔ mg/min without mixing units.
Not started
mcg/kg/min to mL/hr Infusion Rates
Move between an authorised mcg/kg/min dose rate and mL/hr using the verified dosing weight and current concentration, then reverse-check the represented dose rate.
Not started
IV Medication Rate Change Calculations
Separate before and after intervals, verify the already-authorised new target and current preparation, then recalculate the represented medication rate, amount and pump mL/hr without choosing the titration step.
Need something else?
Keep moving without losing your place
PractiseTest this skillOpen the practice library and choose the lesson or mixed set you need.Practice library CalculateNeed the answer now?Jump to the clinical calculator hub without opening a new tab.Browse calculators UnderstandRead the explanationUse Guides for formulas, worked examples, limitations and references.Browse Guides
Lesson summaries
What each IV Calculations lesson teaches
A short recap of every lesson in this topic: the key idea, a worked example and the mistake students make most often. Open any lesson for the full step-by-step teaching and its four levels of practice.
IV Volume, Time & Rate BasicsVolume, time and rate form one relationship with three arrangements. Knowing any two gives the third, so rather than memorising three formulas it is easier to remember that a rate is a volume shared across a time.
Volume, time and rate form one relationship with three arrangements. Knowing any two gives the third, so rather than memorising three formulas it is easier to remember that a rate is a volume shared across a time.
Formula
rate = volume ÷ time · volume = rate × time · time = volume ÷ rate
Worked example
1000 mL is to be given over 8 hours.
- 1Rate is a volume shared across a time, so divide.
- 21000 ÷ 8 = 125
- 3Reverse to check: 125 × 8 = 1000 mL.
125 mL/hr
Common mistake
Multiplying volume by time when the question asks for a rate. The unit you are asked for tells you which arrangement to use: mL/hr means a volume divided by hours.
Read the unit of the answer first — it identifies the operation.
IV Pump Rate (mL/hr)A volumetric pump is programmed in millilitres per hour, so any duration given in minutes has to become hours before the division, or the rate will be out by a factor of 60.
A volumetric pump is programmed in millilitres per hour, so any duration given in minutes has to become hours before the division, or the rate will be out by a factor of 60.
Formula
rate in mL/hr = total volume in mL ÷ time in hours
Worked example
250 mL is to be given over 90 minutes.
- 1Convert the time: 90 ÷ 60 = 1.5 hours.
- 2250 ÷ 1.5 = 166.66…
- 3Round at the end, to the precision the pump accepts.
approximately 167 mL/hr
Common mistake
Dividing 250 by 90 and programming 2.8. Dividing by minutes produces mL per minute, not mL per hour.
Convert minutes to hours before dividing, never after.
IV Infusion Time & Finish TimeIf you know the volume and the rate, the time follows. The result arrives as a decimal number of hours, and converting the fractional part into minutes is the step most often skipped.
If you know the volume and the rate, the time follows. The result arrives as a decimal number of hours, and converting the fractional part into minutes is the step most often skipped.
Formula
time in hours = volume ÷ rate · minutes = fractional part × 60
Worked example
500 mL is running at 80 mL/hr.
- 1500 ÷ 80 = 6.25 hours
- 2The whole part is 6 hours.
- 30.25 × 60 = 15 minutes
6 hours 15 minutes
Common mistake
Reading 6.25 hours as 6 hours 25 minutes. The digits after the decimal point are a fraction of an hour, not minutes.
Always convert the decimal remainder into minutes before stating a duration.
Drops per Minute (gtt/min)Without a pump, the rate is counted in drops per minute. The drop factor — supplied by the giving set — states how many drops make one millilitre, which converts a volume into a number of drops.
Without a pump, the rate is counted in drops per minute. The drop factor — supplied by the giving set — states how many drops make one millilitre, which converts a volume into a number of drops.
Formula
gtt/min = (volume in mL × drop factor) ÷ time in minutes
Worked example
1000 mL is to be given over 6 hours using a set with a supplied drop factor of 20 gtt/mL.
- 1Convert the time to minutes: 6 × 60 = 360.
- 21000 × 20 = 20 000 drops in total.
- 320 000 ÷ 360 = 55.55…
- 4Drops are counted whole, so round at the end.
approximately 56 gtt/min
Common mistake
Leaving the time in hours. Because the answer is per minute, the denominator has to be minutes.
The drop factor comes from the giving set in use and is always supplied, never assumed.
Calculated Medication Amount Over TimeRunning an infusion for a period delivers a calculable amount of drug. Multiplying the rate by the time gives the volume, and multiplying that volume by the concentration gives the amount of medicine in it.
Running an infusion for a period delivers a calculable amount of drug. Multiplying the rate by the time gives the volume, and multiplying that volume by the concentration gives the amount of medicine in it.
Formula
volume = rate × time · amount = volume × concentration
Worked example
An infusion of concentration 2 mg/mL runs at 25 mL/hr for 4 hours.
- 1Volume: 25 × 4 = 100 mL
- 2Amount: 100 × 2 = 200 mg
100 mL delivered, containing 200 mg
Common mistake
Multiplying the rate by the concentration and then by time in the wrong order, or losing track of which figure is a volume and which is an amount. Labelling each intermediate value with its unit prevents it.
Find the volume first, then convert that volume into an amount.
Medication Rate (mg/hr & mg/min)A pump rate in mL/hr and a medication rate in mg/hr describe the same infusion in different units. The concentration converts between them, which is why the same infusion can be talked about in two ways without either being wrong.
A pump rate in mL/hr and a medication rate in mg/hr describe the same infusion in different units. The concentration converts between them, which is why the same infusion can be talked about in two ways without either being wrong.
Formula
mg/hr = mL/hr × concentration in mg/mL · mg/min = mg/hr ÷ 60
Worked example
An infusion of concentration 4 mg/mL is running at 15 mL/hr.
- 115 × 4 = 60 mg/hr
- 2For a per-minute rate: 60 ÷ 60 = 1 mg/min
60 mg/hr, which is 1 mg/min
Common mistake
Reporting a medication rate in mL/hr, or a pump rate in mg/hr. The two are only interchangeable once the concentration has been applied.
State which rate you are quoting — the volume the pump delivers, or the drug that volume contains.
mcg/kg/min to mL/hr Infusion RatesA rate written per kilogram per minute has to travel through several conversions before a pump can use it: weight turns it into a dose per minute, time turns that into a dose per hour, and concentration turns the dose into a volume.
A rate written per kilogram per minute has to travel through several conversions before a pump can use it: weight turns it into a dose per minute, time turns that into a dose per hour, and concentration turns the dose into a volume.
Formula
mcg/min = mcg/kg/min × weight · mcg/hr = mcg/min × 60 · mL/hr = mcg/hr ÷ concentration in mcg/mL
Worked example
A supplied rate of 3 mcg/kg/min for a patient weighing 70 kg, using a preparation of concentration 400 mcg/mL.
- 1Per minute: 3 × 70 = 210 mcg/min
- 2Per hour: 210 × 60 = 12 600 mcg/hr
- 3Volume: 12 600 ÷ 400 = 31.5
31.5 mL/hr
Common mistake
Mixing micrograms and milligrams part-way through. Convert the concentration into the same unit as the dose before the final division.
Work through the chain one conversion at a time and label every intermediate value.
IV Medication Rate Change CalculationsWhen a supplied rate changes, the concentration of the bag has not changed — only the volume being delivered each hour. Recalculating means applying the same concentration to the new rate rather than starting the whole problem again.
When a supplied rate changes, the concentration of the bag has not changed — only the volume being delivered each hour. Recalculating means applying the same concentration to the new rate rather than starting the whole problem again.
Formula
new mg/hr = new mL/hr × concentration in mg/mL
Worked example
An infusion of concentration 2 mg/mL is running at 20 mL/hr. The supplied instruction changes the rate to 30 mL/hr.
- 1Before: 20 × 2 = 40 mg/hr
- 2After: 30 × 2 = 60 mg/hr
- 3The concentration is unchanged; only the rate moved.
40 mg/hr before the change, 60 mg/hr after
Common mistake
Recalculating the concentration as though a rate change altered the bag. Changing a pump rate changes the volume per hour, nothing else.
Identify what actually changed before recalculating anything.