True Negative (TN)

True Negative Calculator with Confusion Matrix

How to Use the True Negative Calculator

This calculator estimates the number of true negatives (TN) based on values from a binary classification task.

To use the calculator:

1. Enter the number of true positives (TP), false positives (FP), and false negatives (FN).
2. Enter the total number of samples used in the classification.
3. Click the button to compute the true negatives (TN).

The result shows the calculated value of TN, the specificity (TN / [TN + FP]), and the corresponding confusion matrix to visualize the classification outcomes.

This tool helps in understanding model performance and evaluating metrics related to negative class predictions.

How True Negative TN Works

                      +------------------+
                      |  Predicted Class |
+----------------+----+------------------+
|                |    |  Negative  |  Positive  |
|  Actual Class  |----+------------+------------+
|                | Neg|   **TN**   |     FP     |
|                |----+------------+------------+
|                | Pos|     FN     |     TP     |
+----------------+----+------------+------------+

How True Negative TN Works

The concept of a True Negative is a fundamental component for evaluating the performance of classification models in artificial intelligence. Its primary function is to measure how effectively a model can correctly identify cases that do not belong to a particular class of interest. This is especially critical in scenarios where false alarms can be costly or disruptive.

The Confusion Matrix

A True Negative is one of the four possible outcomes in a binary classification task, which are typically visualized in a table called a confusion matrix. This matrix compares the model’s predictions against the actual ground truth. The four outcomes are True Positive (TP), False Positive (FP), False Negative (FN), and True Negative (TN). A TN occurs when the actual value is negative, and the model correctly predicts it as negative.

Importance in Model Evaluation

The count of True Negatives is used to calculate several key performance metrics. The most direct one is Specificity (also known as the True Negative Rate), which measures the proportion of actual negatives that are correctly identified. A high number of True Negatives contributes to higher accuracy, but it’s important to analyze it alongside other metrics, as a model could achieve a high TN rate simply by predicting the negative class most of the time, especially in imbalanced datasets.

Practical Application

In practice, maximizing True Negatives is essential in applications where the cost of a false positive is high. For example, in medical screening, a high TN rate ensures that healthy patients are correctly identified as disease-free, preventing unnecessary stress and further testing. In spam filtering, it ensures that legitimate emails are not incorrectly sent to the spam folder. Therefore, understanding and optimizing for True Negatives is a key aspect of building reliable and trustworthy AI systems.

Diagram Explanation

Key Components

• Actual Class: This represents the true, real-world status of the data point (e.g., the email is actually “spam” or “not spam”). It’s the ground truth against which the model’s prediction is measured.
• Predicted Class: This is the output or decision made by the AI model after analyzing the data point.

Matrix Quadrants

• TN (True Negative): The model predicted “Negative,” and the actual class was “Negative.” The model correctly identified something that wasn’t there. For example, an email that is not spam is correctly placed in the inbox.
• FP (False Positive): The model predicted “Positive,” but the actual class was “Negative.” This is a “false alarm.” For instance, a legitimate email is incorrectly sent to the spam folder.
• FN (False Negative): The model predicted “Negative,” but the actual class was “Positive.” The model missed a correct identification. For example, a spam email is incorrectly allowed into the inbox.
• TP (True Positive): The model predicted “Positive,” and the actual class was “Positive.” The model correctly identified what it was looking for.

Core Formulas and Applications

Example 1: Specificity (True Negative Rate)

This formula measures the proportion of actual negatives that are correctly identified by the model. It is a critical metric when the goal is to minimize false alarms, such as in medical diagnostics or spam detection.

Specificity = TN / (TN + FP)

Example 2: Accuracy

Accuracy calculates the overall correctness of the model across all classes. It is the ratio of correct predictions (both True Positives and True Negatives) to the total number of predictions. While useful, it can be misleading in imbalanced datasets.

Accuracy = (TP + TN) / (TP + FP + TN + FN)

Example 3: Negative Predictive Value (NPV)

NPV answers the question: “Of all the instances the model predicted as negative, what proportion were actually negative?” It is important in contexts where a negative prediction must be reliable, such as confirming a component is not defective.

NPV = TN / (TN + FN)

Practical Use Cases for Businesses Using True Negative TN

• Spam Filtering. In email services, True Negatives ensure that legitimate emails are correctly delivered to the inbox instead of being wrongly marked as spam. This maintains user trust and prevents important communications from being missed.
• Fraud Detection. For financial institutions, a high TN rate means that valid transactions are correctly approved without being flagged as fraudulent. This provides a smooth customer experience and reduces the operational burden of investigating false alarms.
• Medical Diagnostics. In healthcare AI, True Negatives correctly identify healthy patients as not having a disease. This prevents unnecessary follow-up procedures, reduces patient anxiety, and allocates medical resources more efficiently.
• Predictive Maintenance. In manufacturing, a True Negative correctly predicts that a piece of equipment will not fail. This prevents unnecessary and costly maintenance interventions on machinery that is functioning correctly, optimizing operational schedules and costs.

Example 1: Financial Transaction Monitoring

Condition: A transaction is legitimate (not fraudulent).
Model Prediction: "Not Fraudulent"
Outcome: True Negative (TN)
Business Use Case: The system correctly processes a valid customer purchase without interruption, ensuring customer satisfaction and preventing the operational cost of investigating a false positive.

Example 2: Quality Control in Manufacturing

Condition: A product is free of defects.
Model Prediction: "Pass"
Outcome: True Negative (TN)
Business Use Case: An automated quality control system correctly identifies a non-defective product, allowing it to proceed in the supply chain without being unnecessarily discarded or sent for manual review. This reduces waste and improves throughput.

🐍 Python Code Examples

This example uses the scikit-learn library to compute a confusion matrix and then extracts the True Negative value. The `confusion_matrix` function arranges the values with TN at the top-left position when using default labels.

from sklearn.metrics import confusion_matrix

# Actual values (0 = negative, 1 = positive)
y_true =
# Predicted values by the AI model
y_pred =

# Generate the confusion matrix
cm = confusion_matrix(y_true, y_pred)

# Extract the True Negative value
# In a 2x2 matrix from scikit-learn:
# TN is at cm
# FP is at cm
# FN is at cm
# TP is at cm
true_negatives = cm

print(f"Confusion Matrix:n{cm}")
print(f"True Negatives (TN): {true_negatives}")

For more complex, multi-class scenarios, you may need to calculate TN for each class in a one-vs-rest manner. This function calculates TP, FP, FN, and TN for a specific class from a multi-class confusion matrix.

import numpy as np

def get_metrics_for_class(cm, class_index):
    """Calculates TP, FP, FN, TN for a specific class."""
    tp = cm[class_index, class_index]
    fp = cm[:, class_index].sum() - tp
    fn = cm[class_index, :].sum() - tp
    tn = cm.sum() - (tp + fp + fn)
    return {'TP': tp, 'FP': fp, 'FN': fn, 'TN': tn}

# Example multi-class confusion matrix
#           Predicted Class
#          (0) (1) (2)
# Actual (0) 50   3   2
# Class  (1)  5  60   5
#        (2)  1   4  70
mcm = np.array([,,])

# Get metrics for Class 0
class_0_metrics = get_metrics_for_class(mcm, 0)
print(f"Metrics for Class 0 (TN): {class_0_metrics['TN']}")

# Get metrics for Class 1
class_1_metrics = get_metrics_for_class(mcm, 1)
print(f"Metrics for Class 1 (TN): {class_1_metrics['TN']}")

Types of True Negative TN

• Standard True Negative. This is a direct, correct prediction where the model identifies an instance as belonging to the negative class. It is the most common form, used in binary and multi-class classification to measure baseline performance.
• Contextual True Negative. In this variation, the meaning of a negative prediction depends on context. For example, in a recommendation system, not recommending a product is a TN, but its value is higher if the user has shown no interest in similar items.
• Conditional True Negative. This type occurs when a negative prediction is only considered correct under specific conditions or thresholds. For example, a fraud detection system might only log a TN if the transaction value is above a certain amount.
• Probabilistic True Negative. Here, an instance is classified as a True Negative if the model’s predicted probability for the positive class is below a defined threshold. This is common in models that output probabilities rather than direct class labels.