False Negative Calculator
Calculate the false negative 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.
False Negatives (FN)
20.00
Actual Positives
100.00
Step by step
Actual positives: total × prevalence
1000 × 0.1
= 100.00
FN: actual positives × (1 − sensitivity)
100.00 × (1 − 0.8)
= 20.00
How it works
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)
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.