A concentration tells how much drug is in a given volume. Every problem in this topic becomes easy once the concentration is written as amount per mL (mg/mL, mcg/mL, units/mL, mEq/mL).

Three ways strength is written

Concentration of a mixed infusion = total drug in the bag ÷ total volume in the bag. For example, heparin 25,000 units in 500 mL = 50 units/mL.

Dilution (C1 × V1 = C2 × V2). When a solution is diluted, the amount of drug does not change. C1 and V1 are the starting concentration and volume; C2 and V2 are the final ones. Diluent to add = V2 − V1.

Titrated infusion formulas

To find the dose a running pump is delivering, reverse the formula: mcg/kg/min = (mL/h × mcg/mL) ÷ (kg × 60).

Rounding: infusion pump rates are commonly set to tenths of a mL/h on smart pumps; follow the pump and policy. The most common error is a missed mg → mcg conversion (× 1,000).

Concentration and titration calculations are used for continuous high-alert infusions and for drugs supplied in percent or ratio strengths.

Worked examples

Example 1 — percent and ratio strengths.

• Grams of dextrose in 500 mL of D10W: 10 g/100 mL × 500 mL = 50 g
• Anaphylaxis: epinephrine 0.5 mg IM. Available: 1 mg/mL (formerly labeled 1:1,000). (0.5 ÷ 1) × 1 mL = 0.5 mL into the mid-outer thigh.
• Cardiac arrest: epinephrine 1 mg IV. Available: 0.1 mg/mL prefilled syringe (formerly 1:10,000). (1 ÷ 0.1) × 1 mL = 10 mL.
• Check: 1:1,000 means 1 g/1,000 mL = 1,000 mg/1,000 mL = 1 mg/mL; 1:10,000 is ten times weaker.

Example 2 — percent strength and dilution (C1V1 = C2V2). Order: magnesium sulfate 4 g IV. Available: 50% vial. For IV use the drug must be diluted to 20% or less.

• 50% = 50 g/100 mL = 0.5 g/mL (500 mg/mL)
• Volume of 50%: 4 g ÷ 0.5 g/mL = 8 mL
• Dilute to 20%: 50% × 8 mL = 20% × V2 → V2 = 400 ÷ 20 = 20 mL final volume
• Diluent to add: 20 − 8 = 12 mL
• Check: 4 g in 20 mL = 0.2 g/mL = 20%. In practice, use a premixed bag from pharmacy whenever available (ISMP high-alert drug), on a pump — for preeclampsia, a 4–6 g loading dose over 20–30 minutes, then 1–2 g/h — with reflexes, respirations, and urine output monitored.

Example 3 — mcg/kg/min to mL/h. Order: dopamine 5 mcg/kg/min. Weight 70 kg. Bag: dopamine 400 mg in 250 mL.

• Concentration: 400 mg ÷ 250 mL = 1.6 mg/mL = 1,600 mcg/mL
• Dose per minute: 5 × 70 = 350 mcg/min
• Dose per hour: 350 × 60 = 21,000 mcg/h
• Rate: 21,000 ÷ 1,600 = 13.125 → 13.1 mL/h
• Dimensional analysis: 5 mcg/kg/min × 70 kg × 60 min/h × 1 mg/1,000 mcg × 250 mL/400 mg = 13.125 mL/h. Same answer.

Example 4 — reverse calculation and titration. Norepinephrine 4 mg in 250 mL is running at 30 mL/h. The order: titrate by 2 mcg/min every 5 minutes to keep MAP 65 mmHg or higher.

• Concentration: 4 mg ÷ 250 mL = 0.016 mg/mL = 16 mcg/mL
• Current dose: 30 mL/h × 16 mcg/mL = 480 mcg/h ÷ 60 = 8 mcg/min
• MAP is 58, so increase to 10 mcg/min: 10 × 60 = 600 mcg/h ÷ 16 = 37.5 mL/h
• Check: 37.5 × 16 = 600; 600 ÷ 60 = 10 mcg/min.

Example 5 — weight-based heparin. Weight 80 kg. Protocol (one common VTE nomogram): bolus 80 units/kg, then 18 units/kg/h. Bolus vial: 1,000 units/mL. Bag: 25,000 units in 500 mL.

• Bolus: 80 × 80 = 6,400 units → 6,400 ÷ 1,000 = 6.4 mL
• Infusion: 18 × 80 = 1,440 units/h
• Concentration: 25,000 ÷ 500 = 50 units/mL
• Rate: 1,440 ÷ 50 = 28.8 mL/h
• Six hours later, the aPTT is low and the protocol says "rebolus 40 units/kg and increase by 2 units/kg/h": rebolus 40 × 80 = 3,200 units (3.2 mL); new rate 20 × 80 = 1,600 units/h ÷ 50 = 32 mL/h.
• Doses and limits differ by protocol (acute coronary syndrome protocols use lower doses with maximums); always use your facility's nomogram.

Example 6 — insulin infusion. DKA; weight 65 kg; order 0.1 units/kg/h. Bag: regular insulin 100 units in 100 mL 0.9% sodium chloride.

• Concentration: 100 units ÷ 100 mL = 1 unit/mL
• Dose: 0.1 × 65 = 6.5 units/h
• Rate: 6.5 ÷ 1 = 6.5 mL/h
• Before starting: potassium must be at least 3.5 mmol/L (mEq/L); if lower, replace potassium and delay insulin. Monitor glucose hourly.

• Wrong concentration chosen (two bag strengths, or 1 mg/mL epinephrine given IV instead of 0.1 mg/mL) → severe overdose
• mg/mcg conversion missed → thousandfold error in vasoactive drugs
• Weight-based order calculated with lb → 2.2-fold overdose
• Drug-specific: heparin → bleeding and HIT; insulin → hypoglycemia and hypokalemia; vasopressors → dysrhythmias, hypertension, tissue ischemia; magnesium → respiratory depression and cardiac arrest

• Use standard concentrations and the smart-pump drug library; avoid programming outside the library ("basic mode").
• Vasoactive infusions: dedicated line or port; a peripheral start in a large proximal vein is acceptable per protocol (do not delay therapy waiting for central access), with a central line preferred for prolonged use; never flush a line containing a vasopressor (the drug in the line becomes a bolus); do not stop abruptly — wean as ordered.
• Heparin: caution with active bleeding, recent surgery, low platelets, or history of HIT (use a non-heparin anticoagulant); interacts with antiplatelets, NSAIDs, and other anticoagulants.
• Insulin infusion: do not start with potassium below 3.5 mmol/L; add dextrose as glucose falls per protocol.
• Dopamine: avoid with MAO inhibitors (hypertensive crisis).
• Magnesium: contraindicated in myasthenia gravis; reduce with kidney impairment; potentiates neuromuscular blockers.
• Ratio labels: US single-drug injectable labels now show mg/mL; ratio expressions persist in local anesthetic–epinephrine combinations (for example, lidocaine with epinephrine 1:100,000) and in older references.

Listed in priority order.

1. Hemodynamic and respiratory monitoring for titrated vasoactive drugs — continuous ECG and frequent or continuous blood pressure (often arterial line), MAP against the ordered target, perfusion, urine output.
2. Independent double check of drug, concentration, dose, weight, pump programming, and line before starting, at every rate change, and at handoff.
3. Titrate only within the ordered parameters (dose range, step size, interval, target); document each change with the client's response.
4. Check the IV site frequently for vasopressor extravasation; if it occurs, stop the infusion, leave the catheter in place initially, and notify for phentolamine per protocol.
5. Laboratory monitoring: aPTT or anti-Xa and platelets (heparin), hourly glucose and potassium (insulin), magnesium level with reflexes and respirations (magnesium).
6. Label each bag and line with drug and concentration; trace lines from bag to client.

• Explain continuous monitoring and why alarms sound; ask the client not to touch pump controls.
• Heparin: report bleeding gums, blood in urine or stool, and new bruising; use a soft toothbrush.
• Insulin infusion: report shakiness, sweating, confusion, or hunger (hypoglycemia).
• Report pain, burning, or swelling at the IV site at once.

• Always convert strength to per mL first
• Percent = g/100 mL (5% = 50 mg/mL; 0.9% NaCl = 9 mg/mL)
• 1:1,000 = 1 mg/mL (IM anaphylaxis); 1:10,000 = 0.1 mg/mL (IV arrest)
• C1V1 = C2V2; diluent to add = V2 − V1
• mcg/kg/min → mL/h: dose × kg × 60 ÷ mcg/mL
• Reverse: mcg/kg/min = mL/h × mcg/mL ÷ (kg × 60)
• Heparin 25,000 units/500 mL = 50 units/mL; 25,000 units/250 mL = 100 units/mL
• Insulin 100 units/100 mL = 1 unit/mL → units/h equals mL/h
• Check potassium (3.5 mmol/L or higher) before an insulin infusion
• Never flush a vasopressor line; extravasation → phentolamine