Calculate F1 score, F-beta scores, and compare precision-recall trade-offs. Understand harmonic mean vs arithmetic mean and optimize your model's threshold for different use cases.
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The F1 score is the go-to metric for evaluating classification models when you need to balance precision and recall. This calculator helps you understand not just the F1 score, but the entire F-beta family of metrics - from precision-focused F0.5 to recall-focused F2. Visualize trade-offs and make informed decisions about your model's threshold.
The F1 score is the harmonic mean of precision and recall, providing a single metric that balances both concerns. Unlike the arithmetic mean, the harmonic mean penalizes extreme imbalances - a model with 100% precision but 0% recall gets F1=0, not 50%. The F-beta generalization lets you weight precision or recall more heavily: F0.5 emphasizes precision (2:1), F2 emphasizes recall (2:1).
F-beta Score Formula
F_β = (1 + β²) × (Precision × Recall) / (β² × Precision + Recall)When you can't report both precision and recall, F1 provides a single number that captures the balance between them.
Unlike accuracy, F1 score doesn't get inflated by a majority class. A model predicting all negatives gets F1=0.
Compare multiple models on a single metric that rewards balance rather than extremes in either direction.
Find the optimal classification threshold by maximizing F1 score on your validation set.
F-beta lets you tune the precision-recall trade-off based on your specific business needs.
Balanced tasks where false positives and false negatives are equally costly. Information retrieval, general classification benchmarks.
When false positives are more costly. Spam filters (don't lose legitimate mail), content moderation (don't censor valid content).
When false negatives are more costly. Cancer screening (don't miss cases), security threats (catch all attacks).
When your cost ratio differs from 1:1, 2:1, or 1:2. Calculate beta from: β = sqrt(cost_FN / cost_FP).
Plot F1 score vs classification threshold to find the optimal operating point for your model.
Use F1 as the scoring metric in cross-validation to select models that balance precision and recall.
The harmonic mean penalizes extreme values. With 90% precision and 10% recall, arithmetic mean gives 50%, but harmonic mean (F1) gives 18%. This reflects that such an imbalanced model is actually quite poor, not average.