Dose and Rate Conversions, Explained
After reading this you can turn a weight-based dose into milligrams, milligrams into millilitres of liquid, and a µg/kg/min infusion order into a pump rate in mL/h, and you will know where the arithmetic can bite you.
Most dosing arithmetic is multiplication and division you already know. The trouble is not the maths. It is keeping the units straight: milligrams versus micrograms, per dose versus per day, minutes versus hours. A single misplaced factor of 1000 turns a safe dose into a dangerous one. This article shows each conversion, the intuition behind it, and a worked example that reproduces the tool's demo numbers exactly.
What these conversions are for
Medicines are prescribed in four common ways, and each needs a small calculation before you can act on it.
- mg/kg
- A dose scaled to body weight. Multiply by weight to get one dose in milligrams.
- mg/kg/day
- A daily total scaled to weight, usually split across several doses. Divide the daily total by the number of doses.
- mg to mL
- A liquid medicine has a concentration in mg/mL. Divide the dose in milligrams by the concentration to get a volume you can measure.
- µg/kg/min
- A continuous infusion rate. Convert to mL/h so an infusion pump can deliver it.
Take a quick hook. A child weighs 20 kg and the order is 15 mg/kg. That is 20 × 15 = 300 mg per dose. If the syrup is 50 mg/mL, you measure 300 ÷ 50 = 6 mL. Two multiplications and one division, and every step is checkable by hand.
When to use it and when not
Use these conversions to check a number you have already been given, to understand a package leaflet, or to see how a prescribed rate translates into a pump setting. They answer the question "does this number make sense?"
They do not decide the dose. The correct dose depends on the drug, the indication, kidney and liver function, age, and interactions. That decision belongs to a prescriber and a pharmacist.
Unit slips are the most common medication errors. Micrograms and milligrams differ by a factor of 1000. "Per dose" and "per day" differ by however many doses you give. Always confirm which unit the order uses before you calculate.
The four formulas
A single dose from a weight-based order:
Here D is the dose in milligrams, w is weight in kilograms, and d is the dose in mg/kg. Weight 20 kg at 15 mg/kg gives D = 300 mg.
A per-dose amount from a daily total split into n doses:
d_{\text{day}} is the daily dose in mg/kg/day and n is the number of doses per day. The daily total is w \times d_{\text{day}}, and dividing by n spreads it evenly.
A volume of liquid medicine from a dose in milligrams:
V is volume in millilitres, D is the dose in milligrams, and c is the concentration in mg/mL. A label reading "250 mg / 5 mL" means c = 50 mg/mL.
An infusion rate in mL/h from a µg/kg/min order:
R is the pump rate in mL/h, r is the rate in µg/kg/min, w is weight in kilograms, and c is the concentration in mg/mL. The 60 converts minutes to hours. The 1000 converts micrograms to milligrams so it matches the concentration. Miss either factor and the answer is off by 60 or by 1000.
A worked example with the demo numbers
Reproducing each mode
Use the tool defaults: weight 20 kg throughout.
- mg/kg to dose. Dose
15mg/kg. D = 20 \times 15 = 300 mg per dose. - mg/kg/day to per-dose. Daily dose
40mg/kg/day over3doses. Daily total 20 \times 40 = 800 mg. Each dose 800 \div 3 \approx 266.7 mg. - mg to mL. Dose
250mg, concentration50mg/mL. Volume 250 \div 50 = 5 mL. - µg/kg/min to mL/h. Rate
5µg/kg/min, weight20kg, concentration50mg/mL. Micrograms per minute: 5 \times 20 = 100. Per hour: 100 \times 60 = 6000 µg/h, which is6mg/h. Volume: 6 \div 50 = 0.12 mL/h.
Every one of these numbers should match what you see after pressing Calculate.
Reading and interpreting the results
The first three modes scale linearly with weight. Double the weight, double the dose or volume. The chart below shows how a 15 mg/kg dose grows with body weight.
Infusions carry an extra idea. The pump rate depends on both weight and concentration. A more concentrated bag needs a slower rate for the same delivered dose, because each millilitre carries more drug. At 5 µg/kg/min and 20 kg, a 50 mg/mL bag needs 0.12 mL/h, but a 25 mg/mL bag (half as strong) needs 0.24 mL/h to deliver the same micrograms.
Common mistakes
The errors below are arithmetic, not judgement, and each one has a recognisable signature.
| Mistake | Effect on the answer | Worked check |
|---|---|---|
| µg read as mg in an infusion | 1000 times too much | 0.12 mL/h becomes 120 mL/h |
| Daily dose used as a single dose | n times too much | 800 mg given instead of 266.7 mg |
| Forgetting the ×60 in an infusion | 60 times too little | 0.12 mL/h becomes 0.002 mL/h |
| Concentration read as total, not per mL | volume off by the pack size | "250 mg / 5 mL" treated as 250 mg/mL gives 1 mL instead of 5 mL |
Sanity-check the size of the answer before trusting it. A liquid dose of a few millilitres is plausible for a syrup. A dose of 60 mL from a single order usually means a unit slipped somewhere. Estimate roughly in your head first, then compute.
How weight uncertainty moves the number
Weight-based doses are only as accurate as the weight. If you estimate a child at 20 kg but the true weight is 18 kg, a 15 mg/kg dose of 300 mg is really 16.7 mg/kg, about 11% high. For most medicines that margin is harmless, but for narrow-therapeutic-index drugs it matters. Weigh the patient rather than guess when the drug is one where small errors count.
Related tools
If you are estimating dates or clearance rather than doses, two other calculators on this site may help. The Pregnancy Due Date Calculator works out a due date from a last period, conception date or IVF transfer. The Blood Alcohol Estimator uses the Widmark equation, which is itself a weight-based calculation much like the mg/kg maths here.
Frequently asked questions
How do I read a label like "250 mg / 5 mL"?
Divide to get the concentration: 250 ÷ 5 = 50 mg/mL. That is the number to enter. It means every millilitre contains 50 mg of drug.
Why does a stronger bag need a slower pump rate?
Because each millilitre of a stronger bag carries more drug. To deliver the same micrograms per minute you move less fluid. At 50 mg/mL you need 0.12 mL/h; at 100 mg/mL you need only 0.06 mL/h.
Does the number of doses per day change the total?
No. The daily total w \times d_{\text{day}} stays the same. More doses per day just makes each individual dose smaller. Splitting 800 mg into 4 doses gives 200 mg each instead of 266.7 mg for 3.
Can I use these formulas for adults and children alike?
The arithmetic is the same. The judgement is not. Many drugs have a maximum adult dose that caps the mg/kg calculation, so a 90 kg adult does not simply get 4.5 times a 20 kg child's dose. Check the leaflet for a ceiling.
What if my answer looks far too large or small?
Suspect a unit slip. A factor of 1000 usually means µg confused with mg. A factor of 60 in an infusion means the minutes-to-hours step was dropped. Recompute slowly and confirm with a pharmacist.
These conversions are an educational estimate, not medical advice. Always double-check against the package leaflet or a pharmacist, and consult a professional for decisions about your health.
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