True Negative Calculator
Calculate the true negative count from a confusion matrix and classification results.
Inputs
Fraction of the population that is truly positive.
True negative rate of the test/model.
True Negatives (TN)
810.00
Actual Negatives
900.00
Step by step
Actual negatives: total × (1 − prevalence)
1000 × (1 − 0.1)
= 900.00
TN: actual negatives × specificity
900.00 × 0.9
= 810.00
How it works
True negatives are correctly identified negative cases: TN = total_population × (1 − prevalence) × specificity. Here, (1 − prevalence) is the number of truly negative individuals in the population, and specificity is the fraction of those the test correctly identifies as negative. TN is the basis of specificity and negative predictive value, and along with TP, FP, and FN completes the full 2×2 confusion matrix for a given population.
Formula
TN = total * (1 - prevalence) * specificity
- N
- Total population
- \pi
- Prevalence (fraction truly positive)
- Sp
- Specificity (true negative rate)
Frequently Asked Questions
Why is TN often the largest confusion matrix cell?
When the condition being tested for is rare (low prevalence), the vast majority of the population is truly negative, so even a moderately specific test will correctly classify a large absolute number of true negatives.
How is TN used to calculate NPV?
Negative Predictive Value (NPV) = TN / (TN + FN), so a higher TN count relative to FN increases confidence that a negative test result truly means the condition is absent.
Does population size affect the TN rate?
No — specificity itself (TN rate) is a property of the test/model, independent of population size; only the absolute TN count scales with total population, not the underlying rate.