# Accuracy Calculator

URL: https://speedycalculator.com/calculators/statistics/accuracy/
Last updated: 2026-10-30

> The accuracy calculator works out how often a test or classifier is right – from a confusion matrix (TP, FN, FP, TN), from sensitivity, specificity and prevalence, or as 100% minus the percent error of a measurement compared with an accepted value.

## Inputs

- Method
- True positives (TP)
- False negatives (FN)
- False positives (FP)
- True negatives (TN)
- Sensitivity (%)
- Specificity (%)
- Prevalence (%)
- Observed (measured) value
- Accepted (true) value

## Results

- Accuracy
- Sensitivity (true positive rate)
- Specificity (true negative rate)
- Balanced accuracy
- Error rate (misclassification)
- Precision / positive predictive value
- Prevalence in the table
- Total cases
- Percent error
- Absolute error (observed − accepted)

## Formula

```
Accuracy = (TP + TN) ÷ (TP + TN + FP + FN)
Accuracy = Sensitivity × Prevalence + Specificity × (1 − Prevalence)
Percent error = |Observed − Accepted| ÷ |Accepted| × 100%, Accuracy = 100% − percent error
```

## Explanation

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

SituationBetter measureClasses roughly balancedAccuracyPositive class rare (under 10%)Balanced accuracy, sensitivity, precision, F1Measuring instrument vs referencePercent error (accuracy = 100% − error)Test used in a different populationRecalculate with that population's prevalence

### Inputs explained

FieldWhat to enterMethodChoose one: Confusion matrix counts, Sensitivity, specificity and prevalence, Measured vs accepted value (percent error)True positives (TP)A numberFalse negatives (FN)A numberFalse positives (FP)A numberTrue negatives (TN)A numberSensitivityIn %SpecificityIn %PrevalenceIn %Observed (measured) valueA numberAccepted (true) valueA 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]

## 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.

## FAQ

**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.


## Sources

- [CDC – Sensitivity, specificity and predictive values (Principles of Epidemiology)](https://www.cdc.gov/csels/dsepd/ss1978/lesson5/section1.html)
- [scikit-learn – Model evaluation: classification metrics](https://scikit-learn.org/stable/modules/model_evaluation.html)
- [NIST/SEMATECH e-Handbook of Statistical Methods](https://www.itl.nist.gov/div898/handbook/)