Calculator
Example data table
| Scenario | Inputs | Computed sides | Perimeter |
|---|---|---|---|
| Three sides | a=5, b=7, c=9 | a=5, b=7, c=9 | P=21 |
| Two sides + angle | a=8, b=6, θ=45° | c≈5.662 | P≈19.662 |
| Coordinates | A(0,0), B(4,0), C(0,3) | AB=4, BC=5, CA=3 | P=12 |
Formula used
- Perimeter (three sides): P = a + b + c
- Two sides with included angle: compute the third side using c² = a² + b² − 2ab·cos(θ), then P = a + b + c.
- Coordinates: compute each side via distance d = √((x₂−x₁)² + (y₂−y₁)²), then add three distances.
- Validation: a triangle must satisfy a+b>c, a+c>b, b+c>a.
How to use this calculator
- Select an input mode: sides, sides+angle, or coordinates.
- Enter your values and set precision if needed.
- Enable “Show steps” to display working and checks.
- Click “Calculate Perimeter” to see the result above the form.
- Use “Download CSV” or “Download PDF” to export your worksheet.
Professional notes
Why perimeter is a practical metric
Triangle perimeter is the total boundary length, useful for fencing, trim, and layout checks. In workshops, a 0.5% measuring error on each side can shift the final perimeter enough to misestimate material orders. For a 5–7–9 triangle, a ±0.05 unit drift per side changes P by ±0.15 units, which scales quickly across repeated cuts.
Choosing the right input mode
The calculator supports three modes to match real data sources. Use “Three Sides” when you directly measured edges. Use “Two Sides + Included Angle” for hinged assemblies, where the included angle is known from a protractor or CAD constraint. Use “Coordinates” when points come from mapping, surveying, or graphing tasks. For example, entering a=8, b=6, θ=45° produces c≈5.662 and P≈19.662, matching the sample table. This is handy when only two edges and an angle are measurable.
Data validation you should not skip
Not every triple of numbers forms a triangle. The triangle inequality prevents degenerate or impossible shapes: each pair of sides must exceed the third. When data violates this rule, perimeter is not meaningful because the shape cannot close. Coordinates are also checked implicitly; nearly collinear points can yield very small area and unstable rounding.
Precision, units, and rounding behavior
Perimeter is computed in the same unit as your inputs, so keep units consistent across sides. Precision controls rounding in the displayed result and downloads. If you plan to sum many perimeters, keep extra decimals during intermediate work, then round at the end to reduce cumulative rounding bias.
Reading the plotted triangle
The Plotly view draws the triangle using your inputs, so you can visually confirm orientation and relative side lengths. Sides mode reconstructs a valid triangle on a baseline; SAS mode uses the included angle to place the third vertex; coordinates mode plots your exact points. If plotting fails, it usually indicates invalid geometry.
Exporting results for reports
CSV export is ideal for spreadsheets and audit trails, capturing inputs, computed sides, and perimeter with a timestamp. PDF export creates a shareable worksheet, including calculation steps when enabled. For teams, exported files make peer review easier and help standardize how measurements are documented.
FAQs
1) Can I use decimals and fractions?
Yes. Enter decimals directly. For fractions, convert to decimals first (for example, 3/8 = 0.375). The calculator validates that all sides are positive and that a valid triangle can be formed.
2) What does “included angle” mean in SAS mode?
It is the angle between the two entered sides. The third side is computed with the law of cosines, then the perimeter is the sum of all three sides.
3) Why do I see a triangle inequality error?
Your values cannot close into a triangle. At least one side is too long compared with the other two. Recheck measurements, units, or angle range.
4) How is perimeter computed from coordinates?
Each side length is calculated using the distance formula between point pairs (AB, BC, CA). The perimeter is the sum of those three distances.
5) Why doesn’t the chart appear sometimes?
Plotting is skipped when geometry is invalid or produces an impossible coordinate reconstruction. Fix inputs until the triangle is valid, then the visualization will render automatically.
6) What is included in CSV and PDF exports?
Exports include timestamp, mode, unit, inputs, computed side lengths, and perimeter. If you enable steps, the PDF also includes the step-by-step working and validation checks.