Introduction
The tan inverse calculator (also called an arctan calculator) finds the angle when you know the tangent value. In simple terms, if you know the ratio of two sides of a right triangle, this tool tells you the angle between them. It gives results in both degrees and radians, shows exact values like π/4, and walks you through each step of the solution.
You can use this calculator in three ways. Enter a single number, type in the opposite and adjacent sides of a triangle, or use the two-argument form (atan2) to get angles in any quadrant. The tool also draws a right triangle diagram, plots the angle on a unit circle, and graphs the full arctan function so you can see where your answer falls.
The inverse tangent function, written as tan−1(x) or arctan(x), always returns an angle between −90° and 90° (or −π/2 to π/2 in radians). This is its principal range. For example, arctan(1) = 45° because the tangent of 45° is 1. This calculator gives you fast and accurate answers with clear steps.
How to Use Our Tan Inverse Calculator
Enter a number or side lengths, and this calculator will find the arctan (tan inverse) angle in degrees, radians, or both. It also shows step-by-step work, a right triangle diagram, and a unit circle diagram.
Pick your input method. Click one of the three tabs at the top: "Single Value" to type one number, "Opposite / Adjacent" to enter two triangle sides, or "Two-Argument (atan2)" to enter Y and X values for a full-range angle.
Single Value tab: Type a number or math expression into the input box. You can use decimals like 0.5, expressions with square roots like 1/sqrt(3), or click one of the preset buttons for common values. Press the "Random" button to try a random number.
Opposite / Adjacent tab: Enter the length of the opposite side and the adjacent side of a right triangle. The adjacent side cannot be zero. The calculator divides opposite by adjacent and finds the angle.
Two-Argument (atan2) tab: Enter a Y value and an X value. This mode uses the signs of both numbers to place the angle in the correct quadrant, giving results from −180° to 180°.
Output Units: Choose "Both" to see degrees and radians, or pick "Degrees only" or "Radians only" to show just one.
Rounding Precision: Use the dropdown to set how many decimal places appear in your answer, from 0 up to 15 or maximum accuracy.
Calculate: Click the "Calculate" button or press Enter to get your result. Click "Clear All" to reset every field back to its default value.
What Is Tan Inverse (Arctan)?
Tan inverse, also called arctan or arctan(x), is the opposite of the tangent function. Tangent takes an angle and gives you a ratio. Tan inverse does the reverse: it takes a ratio and gives you the angle. The symbol for it is tan−1(x) or arctan(x).
How Does It Work?
In a right triangle, the tangent of an angle equals the opposite side divided by the adjacent side. If you already know that ratio but need to find the angle, you use tan inverse. For example, if the opposite side is 5 and the adjacent side is 5, the ratio is 1. Plugging that in gives you tan−1(1) = 45°. That means the angle is 45 degrees.
Output Range
The tan inverse function always returns an angle between −90° and 90° (or −π/2 to π/2 in radians). It never gives a result outside that range. You can put in any number (positive, negative, large, or small), and you will always get an angle within those bounds.
What Is atan2?
Regular arctan only tells you an angle in a half-circle. The atan2 function is a two-argument version that uses both an x-value and a y-value. Because it looks at the signs of both numbers, it can place the angle in the correct quadrant. This gives you the full range from −180° to 180°. It is especially useful in programming, physics, and navigation.
Common Tan Inverse Values
Some inputs produce well-known exact angles:
- tan−1(0) = 0°
- tan−1(1/√3) = 30°
- tan−1(1) = 45°
- tan−1(√3) = 60°
Negative inputs give the same angles but negative. For instance, tan−1(−1) = −45°.
Where Is Tan Inverse Used?
Tan inverse shows up in many real-world tasks. Engineers use it to find angles in structures. Physicists use it to calculate directions of forces or to resolve components in projectile motion. Game developers use atan2 to point characters toward a target. Surveyors use it to measure slopes. Any time you know a rise-over-run ratio and need the actual angle, arctan is the tool you reach for.