Accuracy Calculator

Accuracy (ratio)	0.75
Correct predictions (TP + TN)	150
Total predictions	200

What is the Accuracy Calculator?

Accuracy is one of the most common metrics for evaluating a classification model. It measures the fraction of all predictions that the model got right — both correct positive predictions and correct negative predictions. This calculator turns the four cells of a confusion matrix into an accuracy score expressed as both a ratio and a percentage.

How to use it

Enter the four counts from your confusion matrix:

TP (True Positives) — positive cases correctly predicted as positive.
TN (True Negatives) — negative cases correctly predicted as negative.
FP (False Positives) — negative cases wrongly predicted as positive.
FN (False Negatives) — positive cases wrongly predicted as negative.

The calculator returns accuracy automatically. No tool? Just add the four numbers and apply the formula below.

The formula explained

$$\text{Accuracy} = \dfrac{TP + TN}{TP + TN + FP + FN}$$ The numerator counts every correct prediction, while the denominator is the total number of predictions. Multiply by 100 to convert to a percentage.

2x2 confusion matrix showing TP, TN, FP and FN cells — The four confusion-matrix outcomes: correct predictions (TP, TN) in green and errors (FP, FN) in red.

Worked example

Suppose a model produces $TP = 80$, $TN = 70$, $FP = 20$, $FN = 30$. Correct predictions = $80 + 70 = 150$. Total = $80 + 70 + 20 + 30 = 200$. $$\text{Accuracy} = \dfrac{150}{200} = 0.75$$ or 75%.

Accuracy Across Different Scenarios

The same accuracy formula $\text{Accuracy} = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{TN} + \text{FP} + \text{FN}} \times 100\%$ can hide very different model behaviour. The scenarios below each use a total of 100 cases so the percentages are directly comparable.

Scenario	TP	TN	FP	FN	Accuracy
Balanced dataset, good model	45	45	5	5	90%
Imbalanced, majority-negative (rare disease)	2	93	2	3	95%
"Always predict negative" baseline	0	95	0	5	95%
High false positives (over-flagging)	48	22	28	2	70%
High false negatives (missed positives)	20	50	0	30	70%

The key takeaway is the comparison between the second and third rows: a model that does nothing but predict the majority class scores the same 95% as a model that actually detects some positive cases. On a balanced dataset (row 1) accuracy is far more informative. The last two rows show that two models with identical 70% accuracy can fail in opposite, mutually incompatible ways — one floods you with false alarms, the other quietly misses positives.

Interpreting Your Accuracy Score

Accuracy is the fraction of all predictions the classifier got right — both positives and negatives. An accuracy of 90% means 9 out of every 10 cases were labelled correctly, and the complementary error rate is $100\% - 90\% = 10\%$. It is intuitive and easy to communicate, which is exactly why it is so often misread.

Always compare to the no-information baseline. The most honest sanity check is the majority-class baseline: the accuracy you would get by always guessing the most common class. If 95% of your cases are negative, a classifier that blindly predicts "negative" every time already scores 95%. A real model must beat that baseline to be worth anything — a 95% accuracy is impressive on a 50/50 split and worthless on a 95/5 split.

When high accuracy is misleading. On strongly imbalanced data, accuracy is dominated by the majority class. A fraud detector, rare-disease screen or defect detector can report 99% accuracy while catching almost none of the rare positive cases that actually matter. In these settings the cost of a false negative and a false positive is usually very different, and a single overall percentage cannot capture that.

Metrics that complement accuracy:

Precision — of the cases predicted positive, how many really were: $\text{TP}/(\text{TP}+\text{FP})$. Use it when false positives are costly.
Recall (sensitivity) — of the actual positives, how many you caught: $\text{TP}/(\text{TP}+\text{FN})$. Use it when missing a positive is costly.
Specificity — of the actual negatives, how many you correctly cleared: $\text{TN}/(\text{TN}+\text{FP})$.
F1 score — the harmonic mean of precision and recall, a single number balancing the two on the positive class.
Balanced accuracy — the average of sensitivity and specificity, which corrects for class imbalance and is the better headline figure when classes are skewed.

For the balanced example above (TP=45, FP=5, FN=5), recall and precision are both $45/50 = 90\%$, so accuracy, precision and recall agree — a sign the dataset is well balanced. When they diverge sharply, trust the per-class metrics over the single accuracy number. This is general technical information, not a substitute for domain-specific evaluation of your particular problem.

Definitions & Glossary

True Positive (TP): A positive case that the model correctly predicted as positive (e.g., a sick patient flagged as sick).
True Negative (TN): A negative case that the model correctly predicted as negative (e.g., a healthy patient cleared as healthy).
False Positive (FP): A negative case wrongly predicted as positive — a false alarm. Also called a Type I error.
False Negative (FN): A positive case wrongly predicted as negative — a miss. Also called a Type II error.
Confusion matrix: A 2×2 table cross-tabulating predicted versus actual classes, with TP, TN, FP and FN as its four cells. It is the source of nearly all classification metrics.
Accuracy: The proportion of all predictions that are correct: $(\text{TP}+\text{TN})/(\text{TP}+\text{TN}+\text{FP}+\text{FN})$, usually expressed as a percentage.
Error rate: The proportion of predictions that are wrong: $(\text{FP}+\text{FN})/(\text{TP}+\text{TN}+\text{FP}+\text{FN}) = 1 - \text{Accuracy}$.
Precision: Positive predictive value: $\text{TP}/(\text{TP}+\text{FP})$ — how trustworthy a positive prediction is.
Recall: Sensitivity or true positive rate: $\text{TP}/(\text{TP}+\text{FN})$ — how many actual positives were found.
Specificity: True negative rate: $\text{TN}/(\text{TN}+\text{FP})$ — how many actual negatives were correctly identified.
F1 score: The harmonic mean of precision and recall: $2 \cdot \frac{\text{precision} \cdot \text{recall}}{\text{precision} + \text{recall}}$, a single balanced measure of positive-class performance.

FAQ

Is accuracy always a good metric? No. On imbalanced datasets (e.g. 95% of cases are negative) a model can score high accuracy by always predicting the majority class. Check precision, recall and F1 too.

What range does accuracy take? Between 0 (every prediction wrong) and 1 (every prediction correct), or 0%–100%.

Does it work for multi-class problems? Yes — treat $TP + TN$ as the total number of correctly classified samples across all classes and the denominator as the total samples.