Likelihood Ratio Positive Calculator
Calculate LR+ from sensitivity and specificity, analyze confusion matrices, convert pre-test probability, solve inverse values, and export reusable diagnostic statistics reports easily for users.
Formula Used
LR+ = Sensitivity ÷ (1 − Specificity)
Sensitivity measures the true-positive proportion among condition-positive cases.
Specificity measures the true-negative proportion among condition-negative cases.
Post-test odds equal pre-test odds multiplied by LR+.
How to Use This Calculator
- Select sensitivity, matrix, or inverse calculation mode.
- Choose percentage or decimal input formatting.
- Enter all required values for the selected mode.
- Add pre-test probability when post-test probability is needed.
- Select your preferred decimal precision.
- Press Calculate to view results and calculation steps.
- Use CSV or PDF buttons for reusable reports.
Understanding Positive Likelihood Ratios
A positive likelihood ratio compares two positive-test probabilities. It combines sensitivity and specificity into one measure. Sensitivity describes detection among truly positive cases. Specificity describes correct rejection among truly negative cases. LR+ uses the false-positive rate in its denominator. That rate equals one minus specificity. Larger LR+ values indicate stronger separation between groups. A value near one changes odds very little. Interpretation still depends on context and study quality.
From Probability to Updated Odds
Likelihood ratios work naturally with odds rather than probability. Pre-test probability first converts into pre-test odds. Multiply those odds by the calculated LR+. The result becomes post-test odds. Post-test odds can then return to probability. This workflow shows how evidence changes an initial estimate. It also keeps prevalence separate from test sensitivity. The calculator performs every conversion automatically. Users can still inspect each formula step.
Using Confusion Matrix Counts
Raw study counts can generate sensitivity and specificity directly. True positives and false negatives define sensitivity. True negatives and false positives define specificity. Those same counts support several extra metrics. The calculator reports predictive values when counts are supplied. It also reports accuracy, prevalence, and Youden’s J. LR− and diagnostic odds ratio appear automatically. These measures summarize different parts of classification performance. They should not be treated as identical measures.
Checking Inputs and Edge Cases
Valid probabilities must stay between zero and one. Percentage inputs must stay between zero and one hundred. Negative confusion-matrix counts are rejected. Zero denominators are handled before calculation continues. Perfect specificity makes the false-positive rate equal zero. That creates an infinite LR+ mathematically. The calculator displays that result clearly. Inverse mode can solve sensitivity or specificity. The implied answer must remain inside valid probability limits. Export tools preserve results for later analysis. These checks support transparent numerical work.
Example LR+ Values
| Sensitivity | Specificity | False positive rate | LR+ |
|---|
| 70% | 80% | 20% | 3.50 |
| 80% | 90% | 10% | 8.00 |
| 90% | 95% | 5% | 18.00 |
| 95% | 98% | 2% | 47.50 |
Worked Example
Suppose sensitivity is 85%, and specificity is 90%.
LR+ = 0.85 ÷ (1 − 0.90) = 0.85 ÷ 0.10 = 8.5
With 20% pre-test probability, pre-test odds equal 0.25. Post-test odds become 2.125, giving about 68% post-test probability.
Frequently Asked Questions
What is a positive likelihood ratio?
LR+ compares positive-test probability in condition-positive cases against condition-negative cases.
How is LR+ calculated?
Divide sensitivity by one minus specificity.
Can I enter percentages?
Yes. Select percentage format and enter values like 85 and 90.
Can this calculator use TP, FN, TN, and FP?
Yes. Confusion-matrix mode derives sensitivity, specificity, LR+, and extra metrics.
What happens when specificity is 100%?
The false-positive rate becomes zero, so LR+ is mathematically infinite.
What is pre-test probability?
It is the probability estimate used before applying the test result.
How does LR+ change pre-test probability?
Probability converts to odds, multiplies by LR+, then converts back.
Can I solve for sensitivity or specificity?
Yes. Inverse mode solves either value when LR+ and another metric are known.
What do CSV and PDF exports contain?
They include calculated results for saving, sharing, and reporting.