Accuracy is the share of all decisions that turn out correct. For a medical test, spam filter or machine-learning model it is the number of true positives plus true negatives divided by every case tested. For a measuring instrument it describes how close a reading is to the accepted (true) value, which is usually expressed through the percent error.
The calculator offers three methods. With a confusion matrix you type the four counts and get accuracy together with sensitivity, specificity, balanced accuracy, error rate, prevalence and precision. If you only know a test’s sensitivity and specificity, enter the prevalence of the condition in the population you care about – accuracy changes with prevalence because it weights the two rates by how common each group is. The third method compares an observed measurement with an accepted value.
A single accuracy figure can mislead when one class is rare. A test that calls everyone healthy is 99% accurate when 1% of people are ill, yet it finds nobody. That is why balanced accuracy and the separate rates are shown next to it.
How to use the Accuracy Calculator
- Method
- True positives (TP)
- False negatives (FN)
- False positives (FP)
- True negatives (TN)
- Sensitivity
- Specificity
- Prevalence
- Observed (measured) value
- Accepted (true) value
Results update as you type, and everything is calculated in your browser.
How it works
In matrix mode the correct decisions (TP + TN) are divided by the total. In prevalence mode the sensitivity is weighted by the prevalence and the specificity by the share without the condition. In percent-error mode the absolute difference between the observed and accepted values is divided by the accepted value and subtracted from 100%.
Worked example
A screening test is run on 200 people: 45 true positives, 5 false negatives, 10 false positives and 140 true negatives. Accuracy = (45 + 140) ÷ 200 = 92.5%. Sensitivity = 45 ÷ 50 = 90%, specificity = 140 ÷ 150 = 93.33%, so balanced accuracy = 91.67%. Precision is 45 ÷ 55 = 81.82%, and the prevalence in this sample is 50 ÷ 200 = 25%.
Which accuracy measure to use
| Situation | Better measure |
|---|---|
| Classes roughly balanced | Accuracy |
| Positive class rare (under 10%) | Balanced accuracy, sensitivity, precision, F1 |
| Measuring instrument vs reference | Percent error (accuracy = 100% − error) |
| Test used in a different population | Recalculate with that population’s prevalence |
Inputs explained
| Field | What to enter |
|---|---|
| Method | Choose one: Confusion matrix counts, Sensitivity, specificity and prevalence, Measured vs accepted value (percent error) |
| True positives (TP) | A number |
| False negatives (FN) | A number |
| False positives (FP) | A number |
| True negatives (TN) | A number |
| Sensitivity | In % |
| Specificity | In % |
| Prevalence | In % |
| Observed (measured) value | A number |
| Accepted (true) value | A number |
What each result means
- Balanced accuracy = ([Sensitivity (true positive rate)] + [Specificity (true negative rate)])÷2
- Error rate (misclassification) = 100 – [Accuracy]
- Prevalence in the table = ([True positives (TP)] + [False negatives (FN)])÷([True positives (TP)] + [False negatives (FN)] + [False positives (FP)] + [True negatives (TN)])×100
- Total cases = [True positives (TP)] + [False negatives (FN)] + [False positives (FP)] + [True negatives (TN)]
- Percent error = abs([Observed (measured) value] – [Accepted (true) value])÷abs([Accepted (true) value])×100
- Absolute error (observed − accepted) = [Observed (measured) value] – [Accepted (true) value]
Formula
Accuracy = (TP + TN) ÷ (TP + TN + FP + FN)
Accuracy = Sensitivity × Prevalence + Specificity × (1 − Prevalence)
Percent error = |Observed − Accepted| ÷ |Accepted| × 100%, Accuracy = 100% − percent error
Worked example
Inputs — Method: Confusion matrix counts; True positives (TP): 45; False negatives (FN): 5; False positives (FP): 10; True negatives (TN): 140.
Results — Accuracy = 92.5 %; Sensitivity (true positive rate) = 90 %; Specificity (true negative rate) = 93.3333 %; Balanced accuracy = 91.6667 %; Error rate (misclassification) = 7.5 %; Precision / positive predictive value = 81.8182 %; Prevalence in the table = 25 %; Total cases = 200.
Key terms
- Confusion matrix
- A 2 × 2 table of true positives, false positives, false negatives and true negatives.
- Sensitivity
- The share of real positives that the test detects, TP ÷ (TP + FN).
- Specificity
- The share of real negatives correctly cleared, TN ÷ (TN + FP).
- Percent error
- The size of a measurement error relative to the accepted value, in percent.
Frequently asked questions
What is a good accuracy?
It depends on the base rate. With 50/50 classes, 90% is strong; with a 1% positive class, 99% can be achieved by always answering "negative", so look at sensitivity and balanced accuracy too.
How do I calculate accuracy from sensitivity and specificity?
Accuracy = sensitivity × prevalence + specificity × (1 − prevalence). With 90% sensitivity, 95% specificity and 10% prevalence it is 0.9 × 0.1 + 0.95 × 0.9 = 94.5%.
Is accuracy the same as precision?
No. Accuracy is closeness to the true value (or the share of correct decisions); precision is how repeatable results are, or in classification the share of positive calls that are correct.
Can accuracy be negative?
Not as a share of correct decisions. With the percent-error method, an error larger than 100% would give a negative number, which simply means the measurement is off by more than the accepted value itself.
What is balanced accuracy?
The average of sensitivity and specificity. It is not affected by class imbalance, so it is preferred for rare conditions.
How do I turn percent error into accuracy?
Subtract it from 100%. A thermometer reading 98.2 °F when the accepted value is 98.6 °F has a 0.41% error, so it is about 99.59% accurate.
Why does accuracy change with prevalence?
Because it averages sensitivity and specificity weighted by how many people are in each group. A test with poor sensitivity looks better in a population where almost nobody has the condition.