Free Drug Concentration Calculator
Free Drug Concentration Calculator
Convert a total concentration to unbound drug, or back, from the protein binding percentage — because only free drug is active, and for a 95%-bound agent the two differ twentyfold.
Free and total concentration
Protein binding ⇄total 100 mg/L, 95% protein bound, total to free
Formula
- the unbound fraction fu
- (100 − binding%) / 100. At 95% bound fu is 0.05 and the total concentration is twenty times the free one; at 2% bound fu is 0.98 and the two are within 2% of each other
- at zero binding
- fu is 1 and both directions are the identity. That is the only place a factor of exactly 1 belongs, and it is asserted in both directions in this batch’s proofs
- at 100% binding
- the calculation refuses. Free-to-total would be a division by zero, and total-to-free would return zero, which is not a concentration any real agent has. No clinically used antibacterial is 100% bound
- why binding is not a constant
- albumin is the main binding protein, so binding falls when albumin falls. Jongmans and colleagues’ systematic review of cephalosporin binding found lower mean binding in critically ill, dialysis and cardiopulmonary-bypass patients than in healthy volunteers, and cefuroxime binding of 24.6% in critically ill patients with hypoalbuminaemia against 16-28% in plasma generally. Binding can also saturate: ceftriaxone and ertapenem both fall from about 95% to about 85% as the concentration rises
- what this is not
- it is not a measured unbound level. Jongmans and colleagues recommend measuring unbound concentrations directly to optimise exposure in an individual patient, because a population binding percentage applied to one patient’s total level is an estimate with no stated error
Worked example
total 100 mg/L, 95% protein bound, total to free
Unbound fraction = (100 − 95) / 100 = 0.05
100 × 0.05 = 5.000 mg/L free; the total is twenty times the free concentration
Reverse it: a measured free level of 5 mg/L at 95% binding corresponds to a total of 5 ÷ 0.05 = 100 mg/L, so the two directions are exact inverses
Now drop the binding ten points, to 85% — the figure ceftriaxone's own label gives at a plasma concentration of 300 mcg/mL: free becomes 100 × 0.15 = 15 mg/L, three times as much
The same ten-point fall at 30% binding, piperacillin's figure, takes the free concentration from 70 to 80 mg/L — a change of a seventh. Binding dominates the answer only when binding is high
At 0% binding both directions return 100 mg/L unchanged, which is the only place the conversion factor is exactly 1
Protein binding, each figure from the source named
| Agent | Per cent bound | Source |
|---|---|---|
| Meropenem | about 2% | MERREM I.V. US prescribing information, Clinical Pharmacology |
| Piperacillin and tazobactam | about 30% each | ZOSYN US prescribing information, Clinical Pharmacology |
| Ciprofloxacin | about 20-30% (fraction unbound 70-80%) | EUCAST ciprofloxacin rationale document v2.0, 1 January 2021 |
| Amikacin | about 0-11% (fraction unbound 89-100%) | EUCAST amikacin rationale document v3.1, September 2024 |
| Vancomycin | about 55%, by ultrafiltration | Vancomycin hydrochloride US prescribing information |
| Ceftriaxone | 95% below 25 mcg/mL, falling to 85% at 300 mcg/mL | Ceftriaxone US prescribing information, Clinical Pharmacology |
| Ertapenem | about 95% below 100 mcg/mL, falling to 85% at 300 mcg/mL | INVANZ prescribing information, Distribution |
| Cefuroxime | 16-28% in plasma; 24.6% in critically ill hypoalbuminaemic patients | Jongmans 2022 systematic review of cephalosporin binding |
| Cefazolin | about 49-87% depending on the population studied | Jongmans 2022 systematic review of cephalosporin binding |
How much a ten-point fall in binding changes the free concentration
| Binding falls from | To | Free concentration rises by |
|---|---|---|
| 95% | 85% | 3.0× |
| 90% | 80% | 2.0× |
| 55% | 45% | 1.22× |
| 30% | 20% | 1.14× |
| 12% | 2% | 1.11× |
Only free drug is active, and binding is not a constant
A drug bound to albumin is inert. It does not cross a capillary wall, it does not reach the interstitium where most infections sit, and it does not engage a bacterial target. Jongmans and colleagues put it plainly in their 2022 systematic review: only the free fraction has an antibacterial effect. Every published pharmacodynamic target that is written in free terms — the beta-lactam fT>MIC figures, EUCAST’s fAUC/MIC targets for aminoglycosides and quinolones, the SFPT/SFAR recommendation of a free concentration four to eight times the MIC — therefore has to be compared against a free concentration, and almost every assay reports total drug. Almost every PK/PD target in use was derived in animal infection models and in-vitro systems — most often the neutropenic murine thigh model — and the human outcome data behind them are thin: the targets are mostly from animal models and in-vitro systems with limited human outcome validation.
For a weakly bound agent the distinction is a rounding error. Meropenem is about 2% bound, so its total and free concentrations differ by less than the assay’s own imprecision. For a highly bound agent it dominates everything else on the page. Ceftriaxone’s label states 95% binding below a plasma concentration of 25 mcg/mL, so a total level of 100 mg/L is a free level of 5 mg/L; comparing that total level against a free-drug target overstates the exposure twentyfold. Flucloxacillin, ertapenem and teicoplanin sit in the same region. This is not a subtlety — it is a twentyfold error in the only quantity that matters.
The harder point is that the binding percentage moves. Albumin is the main binding protein for the acidic antibacterials, so binding falls when albumin falls, and the free fraction rises correspondingly. Jongmans and colleagues found lower mean binding in critically ill, dialysis and cardiopulmonary-bypass patients than in healthy volunteers, with wide variation between individuals, and reported cefuroxime binding of 24.6% in critically ill patients with hypoalbuminaemia. A second mechanism acts within a single dosing interval: binding saturates. Both ceftriaxone and ertapenem fall from about 95% bound to about 85% as the plasma concentration rises from low to high, which means the free fraction at the peak is not the free fraction at the trough and no single multiplier is right across the whole interval. The arithmetic on this page is exact; the input is not.
Which is why the review’s own recommendation is to measure unbound concentrations rather than to calculate them, where the question matters enough — a highly bound agent, a hypoalbuminaemic patient, a difficult organism. This page is for the common case where only a total level and a published binding percentage exist, and it is honest about what that is worth. Check the albumin before trusting the conversion: the albumin unit converter handles the units.
Frequently asked questions
Why does only free drug matter?
Protein-bound drug cannot leave the circulation or bind a bacterial target, so it contributes nothing to killing. Jongmans and colleagues’ 2022 systematic review states directly that only the free fraction has an antibacterial effect, and recommends measuring unbound concentrations to optimise exposure in individual patients.
How do I convert a total concentration to a free one?
Multiply by the unbound fraction, which is (100 minus the binding percentage) divided by 100. At 95% bound that is 0.05, so a total of 100 mg/L is a free concentration of 5 mg/L. Going the other way, divide instead of multiplying. The two directions are exact inverses, which is asserted in both directions in this batch’s proofs.
Is protein binding the same in every patient?
No, and treating it as a constant is the commonest mistake here. Albumin is the main binding protein, so binding falls in hypoalbuminaemia and in critical illness and the free fraction rises. Jongmans and colleagues found lower mean binding in critically ill, dialysis and cardiopulmonary-bypass patients than in healthy volunteers, with wide individual variation.
Does protein binding change within a dosing interval?
For some agents, yes. Ceftriaxone’s label gives 95% binding below a plasma concentration of 25 mcg/mL falling to 85% at 300 mcg/mL, and ertapenem’s gives about 95% below 100 mcg/mL falling to about 85% at 300 mcg/mL. Binding sites saturate, so the unbound fraction at the peak is higher than at the trough and no single multiplier is right across the whole interval.
Which agents is this worth doing for?
The highly bound ones, where the correction is large: ceftriaxone, ertapenem, flucloxacillin, teicoplanin, daptomycin. For meropenem at about 2% bound and the aminoglycosides at a fraction unbound of 89 to 100% the correction is smaller than the assay’s imprecision and can reasonably be ignored.
Why does the calculator refuse at 100% binding?
Because the free-to-total direction would be a division by zero and the total-to-free direction would return zero, which is not a concentration any real agent has. No antibacterial in clinical use is 100% bound, so the refusal marks an input error rather than a physiological limit.
Related calculators
References
- Jongmans C, Muller AE, Van Den Broek P, et al. An overview of the protein binding of cephalosporins in human body fluids: a systematic review. Front Pharmacol. 2022;13:900551. Open access; source for the spread of binding values between studies and populations and for the statement that only the free fraction has an antibacterial effect.
- Ceftriaxone for injection, USP. US prescribing information, Clinical Pharmacology. Source for 95% binding below 25 mcg/mL falling to 85% at 300 mcg/mL, and a half-life of 5.8 to 8.7 hours.
- INVANZ (ertapenem) for injection. Prescribing information, Distribution and Elimination. Source for about 95% binding below 100 micrograms/mL falling to about 85% at 300 micrograms/mL.
- ZOSYN (piperacillin and tazobactam) for injection. US prescribing information, Clinical Pharmacology. Source for about 30% binding of both components and a half-life of 0.7 to 1.2 hours.
- MERREM I.V. (meropenem for injection). US prescribing information, NDA 50-706/S-022, Clinical Pharmacology. Source for about 2% binding and a half-life of about 1 hour.
- Vancomycin hydrochloride for injection, USP. US prescribing information, Clinical Pharmacology. Source for about 55% binding by ultrafiltration and a half-life of 4 to 6 hours.
- European Committee on Antimicrobial Susceptibility Testing. Amikacin rationale document, version 3.1, September 2024. Source for the fAUC/MIC targets and the fraction unbound; attributes the murine data to the USCAST evaluation (Ambrose et al. 2019).
- European Committee on Antimicrobial Susceptibility Testing. Ciprofloxacin rationale document, version 2.0, 1 January 2021. Source for the fAUC/MIC targets, the fraction unbound, and the total-drug AUC:MIC of 125 that it attributes to Forrest et al. 1993.
- Societe Francaise de Pharmacologie et de Therapeutique and Societe Francaise d’Anesthesie et de Reanimation. Recommandations de Pratiques Professionnelles: optimisation du traitement par beta-lactamines chez le patient de soins critiques. 2018; published in English as Guilhaumou R et al, Crit Care. 2019;23:104. Recommendation R2.2.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/