Calculator Inputs
Example Data Table
| Case | LD50 | Assumed Ratio | Adjustment | Estimated EC50 | Comment |
|---|---|---|---|---|---|
| A | 250 mg/kg | 10 | 1.00 | 25 mg/kg | Moderate screening margin |
| B | 800 mg/kg | 20 | 1.25 | 32 mg/kg | Conservative adjustment applied |
| C | 120 µg/L | 8 | 1.00 | 15 µg/L | Same unit family retained |
Formula Used
1. Ratio Model
The ratio model estimates EC50 from LD50 using an assumed relationship between the lethal endpoint and the effect endpoint.
EC50 = LD50 / (LD50:EC50 ratio × adjustment factor)
2. Hill Response Model
The Hill model estimates EC50 when you know the expected effect percentage at the LD50 dose.
EC50 = LD50 × ((100 / Effect%) - 1)1 / Hill coefficient
Important: LD50 and EC50 measure different endpoints. A true EC50 cannot be proven from LD50 alone. This tool provides a transparent estimate for screening, comparison, or early documentation.
How to Use This Calculator
- Enter the compound name or study label.
- Add the LD50 value from your source data.
- Select the matching LD50 unit.
- Choose the desired output unit.
- Select the ratio model or Hill response model.
- Enter ratio, adjustment, Hill, and effect values as needed.
- Add uncertainty to produce a practical range.
- Press calculate and review the result above the form.
- Use CSV or PDF export for reporting.
About EC50 Estimation From LD50
Purpose of the Estimate
EC50 and LD50 are often compared during early toxicology review. They are not the same measurement. LD50 describes the dose expected to cause death in fifty percent of a tested population. EC50 describes the dose or concentration expected to produce fifty percent of a selected effect. That effect may be enzyme inhibition, growth reduction, immobilization, receptor activity, or another measurable endpoint.
Why Assumptions Matter
A direct conversion is not scientifically fixed. The relationship depends on the organism, route, exposure period, endpoint, compound class, and dose response curve. This calculator therefore uses transparent assumptions instead of hidden rules. The ratio model is useful when your lab, publication, or screening protocol gives an LD50 to EC50 factor. A larger ratio places EC50 farther below LD50. A smaller ratio makes the predicted effect level closer to the lethal level.
Using the Hill Option
The Hill option is helpful when you want a curve based estimate. It uses an assumed effect percentage at the LD50 dose and a slope value. A higher Hill coefficient creates a steeper curve. A lower value creates a slower transition between weak and strong response. This method can show how sensitive the estimate is to the shape of the curve.
Reporting Good Practice
Always report the selected model, ratio, unit, uncertainty range, and endpoint notes. Do not present the output as measured EC50 unless a real assay supports it. Use this tool for preliminary comparison, internal ranking, education, or planning. Confirm final values with experimental EC50 data whenever regulatory, clinical, environmental, or safety decisions are involved.
FAQs
1. Can EC50 be calculated directly from LD50?
No. LD50 and EC50 measure different endpoints. This calculator estimates EC50 using selected assumptions, ratios, or a Hill response model.
2. What does the LD50:EC50 ratio mean?
It describes how many times larger LD50 is than EC50. A ratio of 10 means the estimated EC50 is one tenth of LD50.
3. When should I use the adjustment factor?
Use it when you need extra correction for route, species, safety margin, study quality, or conservative screening assumptions.
4. What is the Hill coefficient?
It controls the steepness of the dose response curve. Higher values produce sharper changes near the EC50 point.
5. Why is an uncertainty range included?
Estimated EC50 values can vary widely. The uncertainty range helps show possible lower and upper values around the main estimate.
6. Can I mix mg/kg and mg/L?
You should avoid mixing dose and concentration units without a valid conversion basis. Keep endpoints within the same study context.
7. Is this suitable for regulatory submission?
Use it only for screening or explanation. Regulatory work usually requires measured EC50 data and documented test methods.
8. What should I include in reports?
Include LD50 source, endpoint, model, ratio, unit, uncertainty, species, exposure route, and a note that the EC50 is estimated.