True Negative Calculator
Calculate the true negative count from a confusion matrix and classification results.
About True Negative Calculator
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)
Worked example
With the default values below, True Negative Calculator returns True Negatives (TN) of 810.00. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Total Populationaccepts 0–1,000,000,000
- 1,000
- Prevalenceaccepts 0–1
- 0.1
- Specificityaccepts 0–1
- 0.9
Results
- True Negatives (TN)
- 810.00
- Actual Negatives
- 900.00
Step by step
- 1Actual negatives: total × (1 − prevalence)= 900.00
- 2TN: actual negatives × specificity= 810.00
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
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.