104 LearnersLast updated on June 25th, 2025
Inverse Tangent Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about inverse tangent calculators.
What is an Inverse Tangent Calculator?
An inverse tangent calculator is a tool to determine the angle whose tangent is a given number. Since trigonometric functions and their inverses involve complex calculations, the calculator helps find the inverse tangent value quickly and accurately. This calculator simplifies the process, saving time and effort.
How to Use the Inverse Tangent Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the tangent value: Input the tangent value into the given field.
Step 2: Click on calculate: Click on the calculate button to get the angle.
Step 3: View the result: The calculator will display the angle in degrees or radians instantly.
How to Calculate the Inverse Tangent?
To find the inverse tangent of a number, we use the arctan function. The inverse tangent of a number x is the angle θ such that tan(θ) = x. θ = arctan(x) This formula allows us to find the angle whose tangent value is x, providing a straightforward method for calculation.
Tips and Tricks for Using the Inverse Tangent Calculator
When using an inverse tangent calculator, a few tips and tricks can help ensure accuracy and ease:
Consider the range of the arctan function, which typically is between -π/2 and π/2 radians or -90° and 90°.
Understand the context of your problem to determine if you need the angle in degrees or radians.
Use decimal precision to interpret the resulting angle accurately.
Common Mistakes and How to Avoid Them When Using the Inverse Tangent Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible for errors to occur when using a calculator.
Mistake 1
Rounding too early before completing the calculation.
Wait until the very end for a more accurate result. For example, you might round 45.29° to 45° before finishing the calculation, but this will be incorrect. You need to remember the decimal part.
Mistake 2
Confusing radians with degrees
Ensure that you are interpreting the result in the correct unit. If the calculator provides the angle in radians, convert it to degrees if necessary, and vice versa.
Mistake 3
Incorrectly interpreting the range of the arctan function
The range of the inverse tangent function is limited to -90° to 90° or -π/2 to π/2 radians. Misunderstanding this range can lead to incorrect conclusions about the angle.
Mistake 4
Relying on the calculator a bit too much for precision
Remember that the result provided by the calculator is an estimate. In real-life situations, additional context or adjustments may be necessary.
Mistake 5
Assuming all calculators will handle all scenarios.
Not all calculators are designed to handle every mathematical function or scenario. Ensure that your calculator is capable of processing inverse trigonometric functions correctly.
Inverse Tangent Calculator Examples
Problem 1
What is the inverse tangent of 1?
Use the formula: θ = arctan(1) θ = 45° or π/4 radians
This means that the angle whose tangent is 1 is 45° or π/4 radians.
Explanation
By using the arctan function, we find that an angle of 45° or π/4 radians has a tangent of 1.
Problem 2
Find the angle whose tangent is 0.5.
Use the formula: θ = arctan(0.5) θ ≈ 26.57° or 0.4636 radians
This means that the angle whose tangent is 0.5 is approximately 26.57° or 0.4636 radians.
Explanation
The arctan function gives us an approximate angle of 26.57° or 0.4636 radians for a tangent of 0.5.
Problem 3
If the tangent is -1, what is the angle?
Use the formula: θ = arctan(-1) θ = -45° or -π/4 radians
The angle whose tangent is -1 is -45° or -π/4 radians.
Explanation
The inverse tangent of -1 results in an angle of -45° or -π/4 radians.
Problem 4
Determine the angle for a tangent value of 2.
Use the formula: θ = arctan(2) θ ≈ 63.43° or 1.107 radians
The angle corresponding to a tangent of 2 is approximately 63.43° or 1.107 radians.
Explanation
The arctan function calculates an angle of about 63.43° or 1.107 radians for a tangent of 2.
Problem 5
What is the angle if the tangent is -0.75?
Use the formula: θ = arctan(-0.75) θ ≈ -36.87° or -0.6435 radians
The angle for a tangent of -0.75 is approximately -36.87° or -0.6435 radians.
Explanation
The inverse tangent function gives an angle of around -36.87° or -0.6435 radians for a tangent of -0.75.
FAQs on Using the Inverse Tangent Calculator
1.How do you calculate the inverse tangent?
2.What is the range of the arctan function?
3.Why do we use the arctan function?
4.How do I use an inverse tangent calculator?
5.Is the inverse tangent calculator accurate?
Glossary of Terms for the Inverse Tangent Calculator
- Inverse Tangent: A mathematical function that determines the angle whose tangent is a given value.
- Arctan: Another name for the inverse tangent function.
- Radians: A unit for measuring angles based on the radius of a circle.
- Degrees: A unit for measuring angles based on dividing a circle into 360 parts.
- Tangent: A trigonometric function that represents the ratio of the opposite side to the adjacent side in a right triangle.
Explore More calculators
![Important Math Links Icon]()
Previous to Inverse Tangent Calculator
![Important Math Links Icon]()
Next to Inverse Tangent Calculator
Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
