Triangle Area from Two Sides

Length of the first side.
Length of the second side.
The angle between the two given sides.
Math Updated 16 Jun 2026

Triangle Area from Two Sides is a mathematics calculator that helps you calculate the area of a geometric shape from its dimensions. The formula used is: Area = ½×s1×s2×sin(θ); Third side c = √(s1²+s2²−2×s1×s2×cos(θ)) (Law of Cosines). Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.

Formula

Area = ½×s1×s2×sin(θ); Third side c = √(s1²+s2²−2×s1×s2×cos(θ)) (Law of Cosines)
  • Triangle Area from Two Sides gives you a fast estimate using your inputs and updates instantly when you change any value.
  • Formula: Area = ½×s1×s2×sin(θ); Third side c = √(s1²+s2²−2×s1×s2×cos(θ)) (Law of Cosines)
  • Input definitions: • Side 1: the numeric side 1 used in the calculation • Side 2: the numeric side 2 used in the calculation • Included Angle (degrees): the numeric included angle (degrees) used in the calculation
  • Manual method: write down each input, apply the formula step by step, then compare your manual result with the calculator output.
  • Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
  • Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
  • Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
  • Practical tip: test a low, medium, and high scenario to understand sensitivity before making decisions.

Example Calculation

Inputs
  • Side 1: 5
  • Side 2: 7
  • Included Angle (degrees): 60

Suppose you enter: Side 1 = 5, Side 2 = 7, Included Angle (degrees) = 60. The calculator applies the formula (Area = ½×s1×s2×sin(θ); Third side c = √(s1²+s2²−2×s1×s2×cos(θ)) (Law of Cosines)) and shows all output values below. Change any input field to immediately see how the result changes.

Frequently asked questions

What is the Triangle Area from Two Sides?
The Triangle Area from Two Sides is a mathematics calculator that helps you calculate the area of a geometric shape from its dimensions. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
When should I use this calculator?
Use this calculator whenever you need a quick, accurate result for the area of a geometric shape from its dimensions without working through the arithmetic manually.
What units should I enter?
Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
How accurate are the results?
Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
How do I interpret the result?
Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.

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