True Positive Calculator
Calculate the true positive count from a confusion matrix and classification results.
Inputs
Fraction of the population that is truly positive.
True positive rate (recall) of the test/model.
True Positives (TP)
80.00
Actual Positives
100.00
Step by step
Actual positives: total × prevalence
1000 × 0.1
= 100.00
TP: total × prevalence × sensitivity
1000 × 0.1 × 0.8
= 80.00
How it works
True positives are the correctly identified positive cases: TP = total_population × prevalence × sensitivity. Prevalence is the fraction of the population that truly has the condition/class, and sensitivity is the fraction of those true cases the test correctly detects. This formula is commonly used to convert population-level statistics (like disease prevalence and test sensitivity from a clinical study) into expected confusion matrix counts for a given population size.
Formula
TP = total * prevalence * sensitivity
- N
- Total population
- \pi
- Prevalence (fraction truly positive)
- Se
- Sensitivity (true positive rate)
Frequently Asked Questions
What's the difference between TP count and sensitivity?
Sensitivity is a rate (TP / actual positives), while TP count is the absolute number of correctly identified positives in a specific population — you need both prevalence and population size to convert one into the other.
Where does 'actual positives' come from?
Actual positives is simply total population × prevalence — the number of individuals who truly belong to the positive class, regardless of what the test/model predicts.
How do I get the other confusion matrix cells?
Use the FP, TN, and FN Calculators with the same total, prevalence, sensitivity, and specificity inputs to build out the complete 2×2 confusion matrix.