F-Beta Score (F₀.₅, F₁, F₂) Weighted Precision-Recall Harmonic Mean Calculator

Compute F_β, F₀.₅, F₁, and F₂ from Precision, Recall, and weight parameter β.

F_2 Weighted Harmonic Score
77.476 %
Balanced F₁ Score (β = 1.0) 79.8 %
Precision-Weighted F₀.₅ Score (β = 0.5) 82.268 %
Recall-Weighted F₂ Score (β = 2.0) 77.476 %
Inputs
⚡ Scenarios:
%
Classifier Precision / Positive Predictive Value (0% to 100%).
%
Classifier Recall / Sensitivity (0% to 100%).
β
Recall weight factor β (0.5 favors Precision, 1.0 balanced F1, 2.0 favors Recall).
Results & Graph
F_2 Weighted Harmonic Score
77.476 %
Balanced F₁ Score (β = 1.0)
79.8 %
Precision-Weighted F₀.₅ Score (β = 0.5)
82.268 %
Recall-Weighted F₂ Score (β = 2.0)
77.476 %

F_2 Weighted Harmonic Score

Graph 1 • F-Beta (F₀.₅ / F₁ / F₂) Score • Domain Architecture & Live Telemetry Maps Precision Pct, Recall Sensitivity Pct, Beta Weight Factor through F-Beta (F₀.₅ / F₁ / F₂) Score Formula.
F_2 Weighted Harmonic Score: 77.476 % F-Beta (F₀.₅ / F₁ / F₂) Score • Invariants & Metrics F_2 Weighted Harmonic Score 77.476 % Balanced F₁ Score (β = 1.0) 79.8 % Precision-Weighted F₀.₅ Scor 82.268 % Recall-Weighted F₂ Score (β 77.476 %
Graph 2 • F_2 Weighted Harmonic Score Across Precision Pct Sweep (40% → 160%) Evaluates F_β = (1 + β²) × (Precision × Recall) / (β² × Precision + Recall) across 7 operating points (current input highlighted).
0 % 43.91 % 87.82 % 60.68 33.60% 68.99 50.40% 74.06 67.20% 77.48 84% 79.83 100.8% 79.83 117.6% 79.83 134.4%
Graph 3 • Joint Sensitivity: Precision Pct × Recall Sensitivity Pct Compares F_2 Weighted Harmonic Score when Recall Sensitivity Pct is shifted +25% (solid) vs. −25% (dashed).
0 % 52.78 % 105.6 % --- Recall Sensitivity Pct @ 75% 84.58 -30% 89.11 -15% 92.58 +0% 95.32 +15% 95.96 +30%
Summary: At 84% Precision and 76% Recall, F_2 is 77.48% (F₀.₅ = 82.27%, F₁ = 79.8%, F₂ = 77.48%).
Summary: At 84% Precision and 76% Recall, F_2 is 77.48% (F₀.₅ = 82.27%, F₁ = 79.8%, F₂ = 77.48%).
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Formula & Mathematical Methodology: F-Beta (F₀.₅ / F₁ / F₂) Score Formula

F_β = (1 + β²) × Precision × Recallβ² × Precision + Recall
F_β = (1 + β²) × (Precision × Recall) / (β² × Precision + Recall)
  • precisionPct: Precision Pct (%)
  • recallSensitivityPct: Recall Sensitivity Pct (%)
  • betaWeightFactor: Beta Weight Factor (β)

Rounding: Internal floating-point calculations run in 64-bit IEEE-754 double precision; display values round to 2–4 decimal places.

Worked Example: Worked Mathematical Example: F-Beta (F₀.₅ / F₁ / F₂) Score

Compute F_β, F₀.₅, F₁, and F₂ from Precision, Recall, and weight parameter β.

  1. Specify the function parameters, matrix entries, or confusion matrix counts.
  2. Apply the closed-form or iterative formula: F_β = (1 + β²) × (Precision × Recall) / (β² × Precision + Recall).
  3. Examine the primary result, error bounds, and 3 interactive SVG plots.
Result: Computes F-Beta (F₀.₅ / F₁ / F₂) Score via F_β = (1 + β²) × (Precision × Recall) / (β² × Precision + Recall).

Frequently Asked Questions

How does the F-Beta Score (F₀.₅, F₁, F₂) Weighted Precision-Recall Harmonic Mean Calculator compute the solution?

It evaluates F_β = (1 + β²) × (Precision × Recall) / (β² × Precision + Recall) directly in your browser and updates three custom SVG visualizations in real time.

Can I solve backwards for an input parameter using Goal Seek?

Yes. Click "🎯 Goal Seek" in the results toolbar to solve backwards for any numeric input field.

Does this calculator run locally offline?

Yes. All calculations run 100% locally in your browser and work offline via the CalculatorGraph PWA.

Mathematics & Statistics · Machine Learning & Classification Metrics

F-Beta Score (F₀.₅, F₁, F₂) Weighted Precision-Recall Harmonic Mean Calculator: inputs, method, and how to read the result

Compute F_β, F₀.₅, F₁, and F₂ from Precision, Recall, and weight parameter β.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Precision Pct: Classifier Precision / Positive Predictive Value (0% to 100%).
  • Recall Sensitivity Pct: Classifier Recall / Sensitivity (0% to 100%).
  • Beta Weight Factor: Recall weight factor β (0.5 favors Precision, 1.0 balanced F1, 2.0 favors Recall).

What the calculation includes

With the default values shown, F_2 Weighted Harmonic Score is 77.476 %. The calculation follows F-Beta (F₀.₅ / F₁ / F₂) Score Formula; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Precision Pct from 84 % to 92.4 % changes F_2 Weighted Harmonic Score from 77.476 % to 78.797 %. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses exact analytical or standard numerical analysis formulations from NIST DLMF.
  • Double-precision floating-point arithmetic has ~15–17 significant decimal digits of precision.

Scope: Global Mathematical & Statistical Standard Check the assumptions and limitations against your situation before relying on the estimate.

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