Tangent Calculator
Calculate tan(x) for any angle
Common Tangent Values
0°
0
30°
√3/3 ≈ 0.577
45°
1
60°
√3 ≈ 1.732
90°
Undefined
180°
0
270°
Undefined
360°
0
About Tangent Function
The tangent function is one of the fundamental trigonometric functions. In a right triangle, tangent of an angle is the ratio of the opposite side to the adjacent side.
Definition
For a right triangle: tan(θ) = opposite / adjacent
In terms of sine and cosine: tan(θ) = sin(θ) / cos(θ)
Properties
- Range: All real numbers (−∞ to +∞)
- Period: 180° (π radians)
- tan(0°) = 0, tan(45°) = 1
- tan(θ + 180°) = tan(θ)
- tan(−θ) = −tan(θ) (odd function)
- Undefined when cos(θ) = 0 (at 90°, 270°, etc.)
Applications
- Physics: Angles of inclination, slopes
- Engineering: Gear ratios, mechanical advantage
- Surveying: Height and distance calculations
- Navigation: Bearing and course calculations
- Architecture: Roof pitch, ramp angles
How to Use This Calculator
Enter the Angle
Input the angle value you want to calculate the tangent for. You can use degrees or radians.
Select Unit
Choose whether your angle is in degrees (°) or radians (rad).
Calculate
Click the "Calculate Tangent" button to get the result. Note that tangent is undefined at 90° and 270°.
Review Results
View the tangent value along with the angle in both degrees and radians, plus related trigonometric values.
Formula
tan(θ) = opposite / adjacent
In a right triangle
Using Sine and Cosine:
tan(θ) = sin(θ) / cos(θ)
Key Relationships:
- tan(θ) = sin(θ) / cos(θ)
- tan(−θ) = −tan(θ) (odd function)
- tan(θ + 180°) = tan(θ) (period 180°)
Common Values:
tan(0°) = 0
tan(30°) = √3/3
tan(45°) = 1
tan(60°) = √3
tan(90°) = Undefined
About Tangent Calculator
The Tangent Calculator calculates tangent values for any angle in degrees or radians. Tangent is the ratio of sine to cosine and is essential in trigonometry, physics, and engineering applications.
When to Use This Calculator
- Trigonometry Problems: Solve trigonometric equations and identities
- Physics Calculations: Calculate slopes, angles of inclination, and forces
- Engineering: Design ramps, roofs, and mechanical systems
- Surveying: Calculate heights and distances
- Verification: Double-check manual calculations
Why Use Our Calculator?
- ✅ Instant Results: Get accurate tangent values immediately
- ✅ Multiple Units: Supports both degrees and radians
- ✅ Undefined Detection: Clearly indicates when tangent is undefined
- ✅ 100% Free: No registration required
- ✅ Mobile Friendly: Works on all devices
Frequently Asked Questions
Why is tan(90°) undefined?
tan(θ) = sin(θ)/cos(θ). At 90°, cos(90°) = 0, so we would be dividing by zero, which is undefined.
What is tan(45°)?
tan(45°) = 1. This is because sin(45°) = cos(45°), so their ratio is 1.
How is tangent used in slopes?
The tangent of an angle equals the slope (rise/run). For example, a 45° angle has tan(45°) = 1, meaning rise = run.
Can tangent be negative?
Yes! Tangent is negative in the 2nd and 4th quadrants (90°-180° and 270°-360°).
What are the tangent values I should memorize?
Key values: tan(0°)=0, tan(30°)=√3/3, tan(45°)=1, tan(60°)=√3, tan(90°)=undefined. Essential for quick calculations!