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In-vitro Release KineticsAll research tools

In-vitro Release Kinetics

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Calibration

Peak areas

Bold = best fit · n = points fitted · grey = under 3 points, never chosen
K-P n: ≤ 0.45 Fickian · 0.45–0.89 anomalous · ≥ 0.89 Case-II
Withdrawal-corrected cumulative release
Untick a point to drop it from every fit — results update instantly

Red = back-calculated accuracy outside 85–115 % (ICH M10).

Peak area + calibration — HPLC/UV peak areas; concentrations come from your calibration line, then × dilution factor.

Concentration — concentration in the release medium is already known.

Already cumulative — cumulative % released, or cumulative amount (divided by drug loaded).

Two columns: concentration (µg/mL), peak area. One standard per row.

A least-squares straight line is fitted; every standard is back-calculated and checked (Analysis → Calibration).

First row = names. A column named time gives sampling times (h) for the columns to its right; add another time column before a formulation that ran on a different schedule.

Paste straight from Excel (Ctrl+V into any cell) or use Import. Tab / Enter move between cells.

V release-medium volume (mL) · Vs volume withdrawn and replaced at each sample (mL) · DF dilution before injection · Load total drug in the system (µg).

Yellow = default value, not yours. The All row sets one value for every formulation.

Remembered per formulation name. After Calculate, edits update every result instantly.

R² of a least-squares line on each model's linearised form. n = points that model used — each model has its own validity window (e.g. Korsmeyer-Peppas only ≤ 60 % release; no log of 0).

A line through 2 points always gives R² = 1, so fits with fewer than 3 points are greyed and never chosen as best.

Korsmeyer-Peppas n: ≤ 0.45 Fickian diffusion · 0.45 < n < 0.89 anomalous (non-Fickian) · ≥ 0.89 Case-II / super Case-II.

Weibull Td = time to 63.2 % release; beyond the last sampling time it is an extrapolation — read with care.

Cumulative_n = C_n × V + Vs × Σ C_i (i = 1…n−1)
% released = Cumulative_n / Drug loaded × 100

Withdrawal correction after Costa & Sousa Lobo (2001). Cumulative-input data is used as given.

Unticked points are left out of every model fit but stay in the tables and the report.

Cumulative release cannot fall, so a point lower than an earlier one is unticked automatically — re-tick it if you disagree.

Back-calculated C = (Area − c) / m. Accuracy % = back-calculated / nominal × 100.

ICH M10 acceptance for calibration standards: 85–115 %. Values outside are shown in red.

This graph changes only the graph you opened. Every other section changes all graphs at once, so a figure set stays consistent.

Settings are remembered in this browser. Export size × resolution = final pixel size (3× ≈ print quality).

Partial: principle, equations and summary tables showing how each number was measured.

Full: every intermediate arithmetic step for every point, formulation and model.

Both print or save as PDF. The .xlsx holds release per time point, R², rate constants and calibration.

Import data

Use each column's dropdown to mark it as Time or a data series (or leave Ignore).

About Release Kinetics

Privacy

All calculation runs in this browser tab; your data is never sent anywhere. Your last grids and settings are kept in this browser's local storage so they come back next visit.

Methods and references

  1. Costa P, Sousa Lobo JM. Modeling and comparison of dissolution profiles. Eur J Pharm Sci 2001;13:123–133. (withdrawal correction, model forms)
  2. Higuchi T. Mechanism of sustained-action medication. J Pharm Sci 1963;52:1145–1149.
  3. Korsmeyer RW, Gurny R, Doelker E, Buri P, Peppas NA. Mechanisms of solute release from porous hydrophilic polymers. Int J Pharm 1983;15:25–35.
  4. Ritger PL, Peppas NA. A simple equation for description of solute release I. J Control Release 1987;5:23–36.
  5. Hixson AW, Crowell JH. Dependence of reaction velocity upon surface and agitation. Ind Eng Chem 1931;23:923–931.
  6. Baker RW, Lonsdale HK. Controlled release: mechanisms and rates. In: Tanquary AC, Lacey RE, eds. Controlled Release of Biologically Active Agents. Plenum; 1974:15–71.
  7. Langenbucher F. Linearization of dissolution rate curves by the Weibull distribution. J Pharm Pharmacol 1972;24:979–981.

How to cite this tool
User manual

How this website works — four steps

  1. Data. Pick the data type (peak area + calibration, concentration, or already cumulative). Paste from Excel into the grids or use Import .xlsx / .csv. Header row = formulation names; a column named time sets the sampling times for the columns to its right. Fill Experiment settings — V, Vs, DF, drug loaded (yellow = default, not your data; the All row sets every formulation at once). Press Calculate.
  2. Analysis. One card per formulation (max release, best model, release mechanism). Tabs show R² of each model, rate constants, cumulative release (% / µg), points used and calibration quality. Untick a point in Points used and every fit updates instantly.
  3. Graphs. All graphs fit on one screen. Click one to open it large. The Format panel beside the graph changes it live: title, axis names, min/max, tick step, decimals, log scale, colours, marker shape/size, lines, legend, fonts and export size. Download PNG/JPEG (3× = print quality), copy into Word / PowerPoint, or view full screen.
  4. Report. Partial or full step-by-step report (print / PDF / HTML), results as .xlsx, and all graphs in one click.

Shortcuts: Alt+1…4 switch steps · Ctrl+Enter calculate · ← / → previous / next graph · Esc back to all graphs.

Formulas used

1. Calibration (ordinary least-squares straight line)

Area = m·C + c m = Σ(x−x̄)(y−ȳ) / Σ(x−x̄)² c = ȳ − m·x̄ R² = [Σ(x−x̄)(y−ȳ)]² / [Σ(x−x̄)² · Σ(y−ȳ)²] Back-calculated C = (Area − c) / m Accuracy % = C_back / C_nominal × 100

2. Concentration from peak area

C_vial = max(0, (Area − c) / m) (areas below the intercept → 0) C_medium = C_vial × DF

3. Withdrawal-corrected cumulative release (Costa & Sousa Lobo, 2001)

Amount_n = C_n × V Cumulative_n (µg) = C_n × V + Vs × Σ(i=1…n−1) C_i Cumulative release_n (%) = Cumulative_n / Drug loaded × 100

Cumulative-input mode skips this step: % values are used as given; amounts are divided by drug loaded × 100.

4. Kinetic models — each is linearised and fitted with the same least-squares line as step 1 (Q = cumulative %, F = Q/100).

ModelLinear form (y vs x)Points usedConstant from slope / intercept
Zero orderQ = Q0 + k0·tallk0 = slope (%/h)
First orderlog(100 − Q) = log Q0 − k1·t / 2.303Q < 100k1 = −slope × 2.303 (1/h)
HiguchiQ = kH·√t + callkH = slope (%/h^0.5)
Korsmeyer-Peppaslog Q = log k + n·log tt > 0, 0 < Q ≤ 60n = slope; k = 10^intercept
Hixson-Crowell(100 − Q)^(1/3) = 100^(1/3) − kHC·tQ < 100kHC = −slope
Weibulllog[−ln(1 − F)] = b·log t − log at > 0, 0 < Q < 100b = slope; Td = 10^(−intercept / slope) (time to 63.2 %)
Baker-Lonsdale3/2[1 − (1 − F)^(2/3)] − F = kBL·tQ < 100kBL = slope (1/h)

5. Release mechanism from Korsmeyer-Peppas n: n ≤ 0.45 Fickian diffusion · 0.45 < n < 0.89 anomalous (non-Fickian) · n ≥ 0.89 Case-II / super Case-II.

6. Best fit = model with the highest R² among fits with at least 3 points.

Rules followed to earn your trust

  1. Self-check on every page load. The engine re-runs a real example study and compares calibration, % release, R², rate constants, best-fit choice and flagged points against an independently hand-built Excel workbook (tolerance down to 10⁻¹²). The badge in the top bar shows Self-check passed or failed; if it fails, do not use the results.
  2. Your data never leaves the browser. All maths runs locally; nothing is uploaded. Saved grids stay only in this browser and can be erased with one click (About).
  3. No hidden defaults. Any setting you did not enter is highlighted yellow, and the status bar warns until you change it.
  4. No stale results. If you change the data after calculating, a banner says so until you recalculate.
  5. Physically impossible points are flagged, not hidden. Cumulative release cannot fall; such points are auto-unticked and shown, and you can re-tick them.
  6. No fake perfect fits. A line through 2 points always gives R² = 1, so fits with fewer than 3 points are greyed and never chosen as best.
  7. Model validity windows respected. Each model only uses points where its equation is defined (e.g. Korsmeyer-Peppas ≤ 60 % release, no log of 0 or negative numbers). The number of points fitted (n) is shown next to every R².
  8. Calibration quality shown. Every standard is back-calculated; accuracy outside 85–115 % (ICH M10) is marked red.
  9. Every number is traceable. The full report prints each intermediate arithmetic step for every point, formulation and model.
  10. Published methods only. Every equation comes from the peer-reviewed references listed in About.
  11. Versioned and citable. Version number and a ready citation are in About, so results can be reproduced later.
  12. Tamper-checked libraries. Chart and Excel libraries load from a CDN with integrity (SRI) hashes; if they fail, tables still work.

Known limits