# T Distribution Calculator

Calculate Student t distribution PDF, CDF, tail probability, two-tail probability, and central area

> Canonical page: https://elysiatools.com/en/tools/t-distribution-calculator

- **Category:** Math & Numbers

- **Keywords:** t distribution, student t, t test, p value, statistics

## Overview

Calculate probabilities for Student t distributions using a t value and degrees of freedom.

## Inputs

- **T Value** (number)
- **Degrees of Freedom** (number)
- **Probability Mode** (select)
- **Decimal Places** (number)

## When to use

- Conducting hypothesis tests (like t-tests) with small sample sizes where the population standard deviation is unknown.
- Determining the p-value of a test statistic to accept or reject a null hypothesis.
- Calculating confidence intervals for sample means in statistical analysis.

## How it works

- Enter your calculated t-statistic in the T Value field.
- Input the Degrees of Freedom based on your sample size (typically n-1).
- Select the desired Probability Mode, such as two-tail, left-tail, right-tail, or central area.
- Adjust the Decimal Places for precision, and the tool will instantly output the corresponding probabilities in JSON format.

## Use cases

- Evaluating the results of a one-sample or two-sample t-test in academic research.
- Quality control testing in manufacturing where sample sizes are limited.
- A/B testing analysis in marketing to determine if performance differences are statistically significant.

## Frequently asked questions

### What are degrees of freedom in a t-distribution?

Degrees of freedom typically represent the sample size minus one (n-1). They determine the exact shape of the t-distribution curve, which approaches a normal distribution as the degrees of freedom increase.

### What is the difference between one-tail and two-tail probabilities?

A one-tail probability (left or right) tests for an effect in a single direction, while a two-tail probability tests for an effect in either direction, splitting the significance level across both tails.

### Can I calculate the p-value using this tool?

Yes, the calculated tail probabilities directly represent the p-value for your t-statistic, helping you determine statistical significance.

### What is the central probability?

The central probability calculates the area under the t-distribution curve between the negative and positive values of your t-statistic, often used for determining confidence intervals.

### How many decimal places can I calculate?

You can configure the output precision from 0 up to 10 decimal places using the Decimal Places setting.

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