What Is a FREE Inverse Tangent Calculator?
A FREE Inverse Tangent Calculator is an online tool that calculates the angle whose tangent equals a given value. Inverse tangent is also called arctangent or tan⁻¹.
It is useful when you know the tangent ratio of a right triangle but need to find the unknown angle.
Inverse Tangent Formula
The basic formula is:θ=tan−1(x)\theta=\tan^{-1}(x)
where:
- θ = the resulting angle
- x = the tangent value
- tan⁻¹ = inverse tangent, or arctangent
θ=tan−1(1)\theta=\tan^{-1}(1)
θ=arctan(0.0)=0.00 rad≈0.0∘\theta=\arctan(\text{0.0})=\text{0.00}\text{ rad}\approx \text{0.0}^\circθ=arctan(0.0)=0.00 rad≈0.0∘
The input to arctan(y/x) is the ratio of y and x coordinates from the point on the unit circle.
y/xy/xy/x
y/xy/xy/xθ = 0.00 radx = 1.00y = 0.00-2y/xθ
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Example
Suppose:tan(θ)=1\tan(\theta)=1
Using inverse tangent:θ=tan−1(1)\theta=\tan^{-1}(1)θ=45∘\theta=45^\circ
Therefore, the inverse tangent of 1 is 45° when the calculator is set to degrees.
What Can a FREE Inverse Tangent Calculator Calculate?
A FREE Inverse Tangent Calculator can help you:
- Calculate arctangent (tan⁻¹) values
- Find an unknown angle from a tangent ratio
- Solve right-triangle problems
- Calculate angles in degrees or radians
- Check trigonometry homework
- Solve geometry, physics, engineering, and surveying calculations
Degrees and Radians
The result can generally be displayed in degrees or radians.
For example:tan−1(1)=45∘\tan^{-1}(1)=45^\circ
or:tan−1(1)≈0.7854 radians\tan^{-1}(1)\approx0.7854\text{ radians}
Common Uses
A FREE Inverse Tangent Calculator is commonly used for:
- 📐 Trigonometry
- 🔺 Right-triangle calculations
- 📊 Geometry
- 🏗️ Engineering
- 📏 Surveying
- ⚙️ Physics
- 🎓 Mathematics education
In simple terms: a FREE Inverse Tangent Calculator takes a tangent value and works backward to find the corresponding angle.
