Arctan Calculator
Use this free arctan calculator to instantly find the inverse tangent of any value. Enter your input and get the result in both degrees and radians within seconds. No manual calculation needed.
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How to Use the Arctan Calculator?
Using this arctan calc is straightforward:
- Enter the value whose inverse tangent you want to find (e.g., 1, 0.75, 4/3, or any decimal).
- Choose your preferred output unit, arctan in degrees or radians.
- Hit the Calculate button.
- Your result appears instantly, along with the full calculation breakdown.
Whether you want to know arctan on a calculator or understand how to calculate arctan step by step, this tool handles both.
What Is Arctan?
Arctan, short for arc tangent, is the inverse function of tangent. If tan(θ) = x, then arctan(x) = θ. It tells you the angle whose tangent equals a given number. In other words, arctan of a value gives you the angle that produces that tangent ratio.
You may also see it written as:
- atan (used in programming languages)
- arctan(x) or tan⁻¹(x) in mathematics
- arctg in some European notations
- arctang or arctanx in textbooks
All of these refer to the same function. Our arctangent calculator handles all forms of input automatically.
Arctan Formula
The basic relationship is:
If tan(θ) = x, then arctan(x) = θ
To convert arctan to degrees, multiply the radian result by (180/π). Our tool does this conversion automatically, so you always get results in both units side by side.
For the atan calculator, the formula applied internally is:
θ = arctan(x) = tan⁻¹(x)
How to Find Arctan on a Calculator
Many students ask how to do arctan on a calculator, especially physical scientific calculators. Here’s the quick method:
- On most calculators, press 2nd (or Shift) → then press the tan key. This activates the tan⁻¹ (inverse tangent) function.
- Type your value and press Enter or =.
- Make sure your calculator is set to degrees mode if you want the answer in degrees, or radians mode otherwise.
If you’re wondering how to put arctan in a calculator app or online tool, simply enter your number in the input box above and click Calculate. That’s all.
For those asking how to find arctan on a calculator for specific values like arctan 4/3, arctan 5/4, arctan 4/5, or arctan -3/4, just type the decimal equivalent into our tool and get the angle instantly.
Arctan Values | Common Reference
Below are some frequently looked-up arctan values for quick reference:
| x | arctan(x) in Degrees | arctan(x) in Radians |
|---|---|---|
| 0 | 0° | 0 |
| 1 | 45° | π/4 |
| √3 | 60° | π/3 |
| 1/√3 | 30° | π/6 |
| -1 | -45° | -π/4 |
| -√3 (arctan -root3) | -60° | -π/3 |
| ∞ | 90° | π/2 |
| -∞ (arctan -infinity) | -90° | -π/2 |
Use the calculator above to find arctan degrees for any custom value — including arctan 7, arctan 10, arctan 1.5, arctan 0.75, arctan 0.1, arctan 1/2, arctan 3/4, arctan 2/3 in degrees, arctan -3/2, arctan -4/3, and more.
Arctan Table
The arctangent table below lists key angle values for quick lookup. This is especially useful for students who need arctan values without a calculator:
| Angle (Degrees) | Angle (Radians) | tan(θ) = x |
|---|---|---|
| -90° | -π/2 | -∞ |
| -60° | -π/3 | -√3 |
| -45° | -π/4 | -1 |
| -30° | -π/6 | -1/√3 |
| 0° | 0 | 0 |
| 30° | π/6 | 1/√3 |
| 45° | π/4 | 1 |
| 60° | π/3 | √3 |
| 90° | π/2 | +∞ |
For values not listed here, like arctan 10 in degrees, arctan 1.5, or arctan 0.1. Use our calculator above for precise results.
Arctan Chart
The arctan chart below summarizes the behavior of the inverse tangent function across common input ranges:
- For x = 0 → arctan(x) = 0°
- For x > 0 → arctan(x) is a positive angle between 0° and 90°
- For x < 0 → arctan(x) is a negative angle between 0° and -90°
- As x → +∞ → arctan(x) → 90°
- As x → -∞ (arctan -infinity) → arctan(x) → -90°
The function is always defined for all real numbers, making it one of the most useful inverse trig functions in mathematics and engineering.
Interactive arctan (inverse tangent) graph — drag the slider to explore values
x
1.0
arctan(x)
45.00°
Asymptote
± 90°
How to Calculate Arctan Manually
Wondering how to calculate arctangent by hand? Here’s the approach:
For simple values (like arctan 1), you can recall from trigonometric identities that tan(45°) = 1, so arctan(1) = 45°.
For values like arctan 4/5 or arctan of 3/4, convert the fraction to a decimal first (0.8 and 0.75 respectively), then use the arctangent formula or a reference table. Our arc tan calculator handles these conversions automatically.
For how to find arc tan of negative values, such as arctan -3/4 or arctan -rad3, the rule is: arctan(-x) = −arctan(x). So the result is simply the negative of the positive counterpart.
Arctan on a Scientific Calculator vs. Online Tool
| Feature | Scientific Calculator | This Arctan Calculator |
|---|---|---|
| Input format | Decimal only (usually) | Decimals, fractions, any real number |
| Output | Degrees or radians (mode-dependent) | Both simultaneously |
| Accessibility | Requires physical device | Works on any device, any browser |
| Step-by-step | ✗ | ✓ |
If you’ve ever struggled with how to do arctan on a calculator or wondered whether your physical calculator gives degrees or radians by default. This online arc tangent calculator removes all that confusion.
Frequently Asked Questions
What is arctan used for?
Arctan is used in geometry, physics, and engineering to find angles when the tangent ratio is known. It is commonly used in navigation, signal processing, and slope calculations.
What is arctan -infinity?
Arctan of negative infinity equals -90° (or -π/2 radians). This represents the lower asymptote of the arctangent function.
What is arctan of 1?
Arctan 1 equals 45° or π/4 radians, because tan(45°) = 1.
Is arctangent the same as tan inverse?
Yes. Arctan(x), arcus tangent, tan⁻¹(x), and atan(x) all refer to the same inverse trigonometric function.
How to find the arctan of a fraction like arctan 1/2?
Convert it to a decimal (0.5), then enter it into the calculator. The result is approximately 26.57°.
What is arctangent 0?
Arctangent 0 = 0°, since tan(0°) = 0.
How do I find arctan in degrees specifically?
This tool defaults to showing arctan in degrees alongside radians. Just enter your value and both units appear together.