Half Maximal Effective Concentration (EC 50 Calculator)
EC50 Calculator
Fit a sigmoidal Hill equation to your agonist dose-response data and calculate EC50, EC10, EC90, Emax, and Hill slope. Supports single measurements, duplicates, or triplicates with weighted nonlinear regression, SEM error bars, and 95% confidence interval.
💡 Quick Summary
Calculate EC50 — the concentration that produces 50% of the maximum effect — by fitting a sigmoidal Hill equation to your agonist dose-response data. Enter % activation directly, % remaining (inverted automatically), or raw assay signal (normalised using vehicle and Emax controls). Supports single measurements, duplicates, or triplicates with weighted nonlinear regression and SEM error bars. Reports EC50 with 95% confidence interval, Emax, Hill slope, EC10, and EC90.
📋 How to Use
- Select your concentration unit, fitting model (3PL or 4PL), and response data type from the options row.
- If using Raw signal: enter the mean vehicle-control signal (0% effect baseline) and the mean Emax-control signal (100% effect reference) in the normalisation panel that appears.
- Choose the number of replicates per concentration (1, 2, or 3). With duplicates or triplicates, the table adds extra columns and displays live Mean ± SD.
- Enter your concentration / response values directly in the table, click Paste from Excel/Sheets to import a copied range, or click Load example data to pre-fill a GPCR agonist cAMP assay dataset.
- Click Fit Curve & Calculate EC50. The fitted sigmoidal curve, EC50 with 95% CI, Emax, Hill slope, R², EC10, and EC90 are displayed with the chart.
- When replicates are provided, error bars on the chart show ± SEM and weighted fitting (1/SD²) is used automatically.
🧮 Formulas & Logic
📊 Result Interpretation
A lower EC50 means the agonist is more potent — it achieves half-maximal activation at a lower concentration. Compare EC50 values between agonists to rank relative potency.
The maximum achievable effect (upper plateau). For a full agonist relative to a reference standard, Emax = 100%. A value significantly below 100% identifies a partial agonist. Use 4PL to detect this accurately.
n = 1 indicates classical single-site receptor activation. n > 1 suggests positive cooperativity or receptor clustering. n < 1 may indicate heterogeneous receptor populations or negative cooperativity.
3PL fixes the baseline at 0% (vehicle = no effect), appropriate for most agonist assays. 4PL fits the baseline freely — use when your vehicle control shows constitutive/basal activity, or for partial agonists.
When replicates are provided, R² is the weighted coefficient of determination (1/SD² weights). R² > 0.99 is excellent; > 0.95 is acceptable; < 0.90 suggests the data may not follow a simple sigmoidal model.
🔬 Applications
- GPCR pharmacology: cAMP, calcium mobilisation, IP-One, BRET/HTRF functional assays
- Nuclear receptor activation: firefly luciferase, β-galactosidase, or GFP reporter gene assays
- Enzyme activation: substrate conversion rate as a function of activator concentration
- Growth factor dose-response: cell proliferation, differentiation, or survival assays
- Neurotransmitter receptor assays: electrophysiology or calcium imaging dose-response
- Environmental ecotoxicology: hormesis curves, phytotoxicity and algal growth stimulation assays
- ELISA calibration: standard curve fitting for quantitative immunoassays
⚠️ Common Mistakes & Warnings
Your concentration range must include at least one point below 20% activation AND at least one above 80% activation. If neither plateau is reached, the fitted EC50 is extrapolated and may be unreliable.
EC50 is a functional potency measure that reflects the entire signal transduction pathway including receptor coupling efficiency, amplification, and assay conditions. It is not the same as the equilibrium dissociation constant Kd.
If your compound does not reach 100% Emax, the 3PL model will give a misleading result because it forces the curve to 100%. Switch to 4PL to let Emax float freely and measure true intrinsic efficacy.
Weighted regression (1/SD²) down-weights concentrations with high variability. An outlier replicate at one concentration will reduce the influence of that point. Inspect individual replicates before fitting to identify obvious errors.
