False Negative Calculator
Calculate the false negative count from a confusion matrix and classification results.
About False Negative Calculator
False negatives are positive cases the model misses and incorrectly labels as negative: FN = total_population × prevalence × (1 − sensitivity). Here, prevalence gives the number of truly positive individuals, and (1 − sensitivity) is the miss rate — the fraction of true positives the test fails to detect. FN is often the most costly error type in screening applications, such as missing a disease diagnosis or letting fraud go undetected.
Formula
FN = total * prevalence * (1 - sensitivity)
- N
- Total population
- \pi
- Prevalence (fraction truly positive)
- Se
- Sensitivity (true positive rate)
Worked example
With the default values below, False Negative Calculator returns False Negatives (FN) of 20.00. 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
- Sensitivityaccepts 0–1
- 0.8
Results
- False Negatives (FN)
- 20.00
- Actual Positives
- 100.00
Step by step
- 1Actual positives: total × prevalence= 100.00
- 2FN: actual positives × (1 − sensitivity)= 20.00
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 are false negatives often more dangerous than false positives?
In many domains (medical screening, safety systems, fraud detection), missing a real positive case (FN) has more severe consequences than a false alarm (FP), since a false alarm can be caught by a follow-up check while a missed case may go unaddressed entirely.
How does sensitivity affect FN count?
FN and sensitivity move in opposite directions — a model with sensitivity close to 1 catches nearly all true positives, driving FN toward zero, while lower sensitivity means more true positives are missed.
How does FN relate to recall?
Recall = TP / (TP + FN), so a higher FN count for a fixed TP directly lowers recall — recall and the miss rate (FN rate) are complementary, summing to 1.