Triangle Calculator

How This Triangle Calculator Works

Calculate triangle area, perimeter and all three interior angles from three valid side lengths using Heron’s formula and the law of cosines. This rebuilt version uses dedicated, calculator-scoped logic rather than the older shared page script. Inputs are validated before any result is produced, the calculation method is shown beside the answer, and supporting figures help you check whether the result is reasonable.

The core method is s = (a+b+c)/2. Area = √[s(s−a)(s−b)(s−c)]. Angles use the law of cosines. The calculator keeps related measurements beside the main answer so you can review more than one geometric property without re-entering the same dimensions on another page.

How to Use the Calculator

1. Measure or enter each dimension requested by the form.
2. Select the unit that applies to all entered lengths. Do not mix centimeters, meters, inches or feet in the same calculation.
3. Select Calculate. Impossible, zero or negative geometric dimensions are rejected instead of being silently corrected.
4. Review the main result and the supporting values. They are included to make the calculation easier to cross-check.
5. Use Copy Result, Share Result or Save Result Image when you need to keep the answer with its context.

Formula and Calculation Method

s = (a+b+c)/2. Area = √[s(s−a)(s−b)(s−c)]. Angles use the law of cosines.

Use one consistent length unit for every dimension in the form. Because these are geometric formulas, the calculator can preserve that unit directly: linear values remain in the selected unit, areas use squared units, and volumes use cubic units. The calculation does not fetch external rates, product specifications or hidden conversion data.

Worked Example

The example demonstrates the method with simple dimensions. Replace those values with your own measurements and keep the unit attached to the result. If you are checking a drawing or physical object, verify that the requested dimension means radius rather than diameter, perpendicular height rather than slant height, and semi-axis rather than full axis where applicable.

Common Uses

• Solve a side-side-side triangle and review its complete basic geometry.
• Check whether three entered lengths satisfy the triangle inequality.
• Calculate area and angles without manually rearranging multiple formulas.

For practical purchasing, fabrication or construction, geometric output is usually a starting quantity rather than an order quantity. Real materials may require allowances for cuts, overlaps, seams, waste, minimum pack sizes, wall thickness or fabrication details. Apply those project-specific adjustments separately instead of hiding them inside the pure geometry formula.

How to Interpret the Result

Read the headline value together with the supporting figures. A surface-area result is easier to verify when slant height, base area, circumference or another related measurement is shown beside it; a volume result is easier to review when the corresponding cross-section or surface value is visible. Keep the dimensions and unit with any copied result so the number remains understandable later. When comparing alternatives, change one measurement at a time. That makes the effect of radius, height, angle or side length much easier to see and helps reveal accidental unit changes.

Displayed decimals are rounded for readability while normal JavaScript floating-point precision is used during the calculation. For a classroom problem, follow the rounding instruction provided with the exercise. For measured work, do not report more precision than your measurements justify.

Important Limitations

The three side lengths must describe a valid non-degenerate Euclidean triangle. Measurement uncertainty and rounded inputs can affect the displayed angle values.

The result is intended for arithmetic and geometry checking. For structural, pressure-containing, safety-critical, regulated or professionally specified work, confirm dimensions and applicable requirements from drawings, standards, manufacturer documentation or a qualified professional before using a calculated quantity for fabrication or purchase.

Privacy, Mobile Results and Downloads

The arithmetic runs in your browser and no sign-in is required. Copy Result creates a text summary, Share Result uses the browser share sheet when available, and Save Result Image creates a clean local graphic of the answer. On screens up to 700 pixels wide, pressing Calculate opens a compact result panel inside the current viewport. The background page is temporarily locked, and the result actions stay attached to the answer so a phone user does not need to scroll down through the article just to find the result.

The saved image contains the calculator title, main result and method rather than a screenshot of the entire page. That makes the result easier to store in a note, worksheet or project discussion without including surrounding navigation or advertising.

Frequently Asked Questions

What is the triangle inequality?

The sum of any two side lengths must be greater than the third side.

Do the angles always add to 180°?

For a valid Euclidean triangle they do, subject only to tiny display rounding differences.

Which formula calculates area?

The calculator uses Heron’s formula because all three side lengths are known.