Tangent Calculator
Find the tangent of any angle in degrees or radians instantly, with the cotangent too.
tan(45°) = 1
tan(45°)
1
Cotangent (1/tan)
1
Only defined when tan θ ≠ 0
Tangent is the ratio of the opposite side to the adjacent side, equal to sin θ / cos θ. It is undefined at 90° and 270°.
Tangent Calculator on True Calculator gives you an instant, accurate answer with no sign-up and no app install. Find the tangent of any angle in degrees or radians instantly, with the cotangent too. Every result shows the formula and a worked example so you can verify the calculation yourself, and all values are computed in your own browser — your numbers never leave your device.
Popular uses: tangent calculator · tan calculator · tangent of an angle
Reviewed by the True Calculator team · Last updated: August 2026
How We Calculate
This calculator uses standard mathematical formulas — the same ones taught in school and used in exams — verified by our team. All calculations are performed instantly in your browser using JavaScript, so no data is sent to any server.
The formulas follow standard mathematical definitions and conventions used in textbooks and by educational boards. Results are rounded transparently and shown with the exact formula on this page.
When to Use This Calculator
Tangent converts slopes into angles and back, which makes it central to Indian construction and surveying. A civil contractor checking a road gradient divides rise by run and reads the angle: a rise of 3 m over 12 m is arctan(0.25) ≈ 14.04°, a comfortable hill-road pitch. Roofers use tangent to set rafter angles from pitch ratios, and tile cutters use it for skirting angles where floors meet stairs. Farmers estimating the height of a palm tree measure its shadow and the sun's angle, then multiply shadow length by the tangent. Photographers and drone pilots estimate coverage angles from altitude and ground distance. Geography students use tangent with clinometers to measure hill and monument heights, and board-exam students use the standard values tan(0°) = 0, tan(30°) ≈ 0.5774 and tan(45°) = 1 as anchors for every tangent problem.
How to Use This Calculator
- Step 1: Choose whether your angle is in degrees or radians.
- Step 2: Enter the angle, such as 45 for 45 degrees.
- Step 3: Read the tangent value — the ratio of opposite side to adjacent side.
- Step 4: The cotangent (1 divided by tangent) is shown alongside when it is defined.
Worked Example
A surveyor in Dehradun measures a 5 m pole's shadow as exactly 5 m at noon. The tangent of the sun's elevation angle is opposite ÷ adjacent = 5 ÷ 5 = 1, and arctan(1) = 45°, so the sun is 45° above the horizon. With a 30-degree elevation, tan(30°) ≈ 0.5774, meaning a 5 m pole casts a shadow of 5 ÷ 0.5774 ≈ 8.66 m. The calculator also shows tan(0°) = 0 — no shadow length at all when the sun is directly overhead, and tan(45°) = 1, the familiar one-to-one slope.
Tips and Common Mistakes
- •Tip 1: Tangent can be any real number — 0 at 0°, 1 at 45°, and huge values as the angle nears 90°.
- •Tip 2: Use opposite ÷ tangent to find the adjacent side when you know the height and angle.
- •Tip 3: Tangent repeats every 180°, so tan(225°) equals tan(45°), both 1.
- ✗Mistake 1: Trying to evaluate tan(90°) — it is undefined because cos(90°) = 0, and the calculator explains this instead of returning a number.
- ✗Mistake 2: Treating a slope of 1 as 100% angle — a 100% gradient is 45°, while a 100° gradient is nearly vertical and meaningless for roads.
Frequently Asked Questions
What is the tangent of an angle?
In a right triangle, tangent is the ratio of the opposite side to the adjacent side, equal to sin θ / cos θ. tan(45°) = 1, meaning the two sides are equal, as in a 45-45-90 triangle.
Why is tangent undefined at 90 degrees?
At 90°, cos θ = 0, and tan θ = sin θ / cos θ means division by zero. The function grows without limit as the angle approaches 90°, so the calculator shows a clear message instead of an invalid number.
What is the range of tangent?
Unlike sine and cosine, tangent can take any real value — from negative infinity to positive infinity. It repeats every 180° instead of 360°.
When would I use tangent in real life?
For slopes and angles of elevation: if a 5 m pole casts a 5 m shadow, the sun's angle is arctan(1) = 45°. Tangent is also used for roof pitches, road gradients and sight-line calculations.
What is cotangent?
Cotangent is the reciprocal of tangent: 1/tan(θ). Since tan(45°) = 1, cotangent is also 1. It is undefined when tangent is 0, such as at 0° and 180°.
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