Angle Calculator

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Angle Calculator & Geometry Tool

1. Missing Triangle Angle

Enter two angles of a triangle to find the third (sum = 180°).

2. Right Triangle Angle (Trigonometry)

Enter two sides to find the angle θ using Inverse Tangent.

3. Degree to Radian Converter

function calculateTriangleAngle() { var a = parseFloat(document.getElementById('triAngleA').value); var b = parseFloat(document.getElementById('triAngleB').value); var resDiv = document.getElementById('triResult'); if (isNaN(a) || isNaN(b)) { resDiv.style.display = 'block'; resDiv.style.backgroundColor = '#fdedec'; resDiv.innerHTML = 'Please enter both angles.'; return; } var c = 180 – (a + b); resDiv.style.display = 'block'; resDiv.style.backgroundColor = '#e8f4fd'; if (c <= 0) { resDiv.innerHTML = 'Invalid Triangle: Angles must sum to 180°. Current sum exceeds or equals 180.'; } else { resDiv.innerHTML = 'The third angle is: ' + c.toFixed(2) + '°'; } } function calculateTrigAngle() { var opp = parseFloat(document.getElementById('sideOpposite').value); var adj = parseFloat(document.getElementById('sideAdjacent').value); var resDiv = document.getElementById('trigResult'); if (isNaN(opp) || isNaN(adj) || adj === 0) { resDiv.style.display = 'block'; resDiv.style.backgroundColor = '#fdedec'; resDiv.innerHTML = 'Please enter valid side lengths (Adjacent cannot be 0).'; return; } var radians = Math.atan(opp / adj); var degrees = radians * (180 / Math.PI); resDiv.style.display = 'block'; resDiv.style.backgroundColor = '#eafaf1'; resDiv.innerHTML = 'Angle θ is: ' + degrees.toFixed(2) + '° (' + radians.toFixed(4) + ' rad)'; } function degToRad() { var deg = parseFloat(document.getElementById('inputDegrees').value); if (!isNaN(deg)) { var rad = deg * (Math.PI / 180); document.getElementById('inputRadians').value = rad.toFixed(5); } } function radToDeg() { var rad = parseFloat(document.getElementById('inputRadians').value); if (!isNaN(rad)) { var deg = rad * (180 / Math.PI); document.getElementById('inputDegrees').value = deg.toFixed(2); } }

Understanding Angles in Geometry

An angle is formed when two rays meet at a common endpoint known as a vertex. In geometry, angles are fundamental to understanding the properties of shapes, particularly triangles and polygons. This angle calculator helps you solve for unknown variables in three distinct ways: missing triangle components, trigonometric relationships, and unit conversions.

Types of Angles

  • Acute Angle: An angle measuring less than 90°.
  • Right Angle: Exactly 90°, typically indicated by a small square in the corner.
  • Obtuse Angle: Measures between 90° and 180°.
  • Straight Angle: Exactly 180°, forming a straight line.
  • Reflex Angle: Measures greater than 180° but less than 360°.

Key Formulas Used

Our calculator uses the following mathematical principles:

  1. Triangle Sum Theorem: The interior angles of a triangle always add up to 180°. Formula: Angle C = 180° – (Angle A + Angle B).
  2. Inverse Tangent (Arctan): In a right-angled triangle, if you know the length of the opposite side and the adjacent side, you can find the angle using: θ = tan⁻¹(Opposite / Adjacent).
  3. Unit Conversion: To convert degrees to radians, multiply by π/180. To convert radians back to degrees, multiply by 180/π.

Practical Examples

Example 1 (Roof Pitch): If you are building a shed and the roof rises 4 feet for every 12 feet of horizontal distance (the run), what is the angle of the roof? Using the Right Triangle Angle tool, enter 4 for the Opposite side and 12 for the Adjacent side. The result is approximately 18.43°.

Example 2 (Drafting): You have a triangular piece of metal where two corners are measured at 60° and 90°. Using the Missing Triangle Angle tool, enter 60 and 90. The calculator will determine the third angle is 30°, confirming it is a standard 30-60-90 triangle.

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