Triangle Area Calculator

Triangle Area Calculator helps you quickly find the area of any triangle — right, isosceles, or scalene —
using base and height or all three sides. Get instant, accurate results with automatic unit conversions between
in², ft², and cm².

Triangle Area Calculator – Find Area Using Base & Height or 3 Sides

The Triangle Area Calculator lets you find the area of any triangle — using base × height or the three sides (Heron’s formula). Enter your measurements in inches, feet, or centimeters, and the tool instantly shows the triangle’s area with real-time unit conversions.

This area of a triangle calculator is ideal for students, architects, engineers, and land surveyors who need quick, accurate triangle area results. You’ll also find triangle area formulas, examples, and advanced options for right triangles and angles below.

Triangle Area Formula (Degrees, Height, or 3 Sides)

Calculating the area of a triangle depends on what information you already have — base and height, three sides, or two sides and the included angle.
The Triangle Area Calculator automatically applies the right formula, but here’s how each one works if you want to calculate it manually.

① Using Base and Height

The most common formula for finding the area of a triangle is:

A = ½ × base × height
Simply multiply the base by the height, then divide by two.
Example: if the base is 10 inches and the height is 8 inches,
A = ½ × 10 × 8 = 40 square inches.

② Using Three Sides (Heron’s Formula)

When you know all three sides but not the height, use Heron’s Formula:

s = (a + b + c) / 2

A = √[s × (s – a) × (s – b) × (s – c)]
Example: For sides 7, 9, and 11 → s = 13.5 → A ≈ 31.4 in².

③ Using Two Sides and Included Angle

If you know two sides and the angle between them, use the trigonometric formula:

A = ½ × a × b × sin(C)
This works perfectly for non-right triangles. For example, if side a = 12 cm, b = 10 cm, and angle C = 45°,
A = ½ × 12 × 10 × sin(45°) ≈ 42.4 cm².

💡 Tip: For right triangles, one leg is the base and the other leg is the height — so you can use the base × height formula directly.

Which Mode Should You Use? Base × Height vs 3 Sides (Heron)

Our Triangle Area Calculator gives you two modes — Base × Height and 3 Sides (Heron) — and each one fits a different case.
Choosing the right one saves time and gives you the most accurate result.

① Base × Height Mode — Simple & Fast

Use this when you already know the triangle’s base and height — for example, a right triangle or when one side is perfectly horizontal.
Just enter those two values and hit Convert.
Tip: The height must be perpendicular to the base (at a 90° angle). If you only know side lengths — skip this mode.

② 3 Sides (Heron) Mode — When You Don’t Know the Height

Choose this mode if you only know the three sides (a, b, c) of your triangle.
The calculator will automatically apply Heron’s Formula to find the area — no height or angle needed.
This is especially useful for irregular or scalene triangles where the height isn’t obvious or easy to measure.

💡 Pro Tip: If you’re working with an angled triangle and know two sides plus the included angle, you can switch to the formula
A = ½ × a × b × sin(C) — or use a triangle area calculator with angle for faster results.

Example Calculations

Let’s look at a few real-world examples to see how each triangle formula works.
These examples use common U.S. and U.K. units (inches, feet, centimeters) to match practical cases like home design, flooring, and geometry class problems.

① Example 1 — Base × Height (Simple Right Triangle)

Suppose you’re measuring a roof section that forms a right triangle.
Base = 10 in, Height = 8 in
Formula: A = ½ × base × height
→ A = ½ × 10 × 8 = 40 in²

That’s about 0.278 sq ft – perfect for small construction or design measurements.

② Example 2 — Three Sides (Heron’s Formula)

You’re working with a triangle where all sides are known, but not the height.
a = 7 in, b = 9 in, c = 11 in
Half-perimeter: s = (7 + 9 + 11) / 2 = 13.5
Area: A = √[13.5 × (13.5 – 7) × (13.5 – 9) × (13.5 – 11)] ≈ 31.4 in²

This method is perfect for scalene triangles or geometry problems without a perpendicular height.

③ Example 3 — Two Sides and Included Angle

Suppose you’re finding the area of a triangle-shaped land plot in the U.K.
a = 12 cm, b = 10 cm, angle = 45°
Formula: A = ½ × a × b × sin(C)
→ A = ½ × 12 × 10 × sin(45°) ≈ 42.4 cm²

Engineers and architects often use this version when working with angle-based designs.

💡 Try this yourself: Enter these values into the calculator above to see how each method produces results instantly — and how switching between inches, feet, or cm changes your total area.

How to Use the Triangle Area Calculator

The Triangle Area Calculator is designed for both quick estimates and accurate geometry solutions.
You can switch between the two main modes — Base × Height or 3 Sides (Heron) — depending on what you already know.

1. Choose your preferred mode (Base × Height or 3 Sides (Heron)).
2. Enter the known values — either base + height, or the three sides (a, b, c).
3. Click Convert to instantly calculate the area in in², ft², and cm².
4. Use Copy results to save, share, or compare different triangle shapes.

💡 Pro Tip: Try 10, 8, 12 as sample sides in Heron mode to see the formula in action and how the area changes when you adjust each side.

The calculator automatically detects your preferred unit — so you can mix inches and centimeters for international projects without worry.

Advanced Uses – Irregular Shapes and Land Area

Many plots and floor layouts are not perfect triangles or rectangles. When working with an
irregular shape or a land area (4 sides), use a practical surveying approach:

• Sketch & split: draw the outline and divide it into triangles (and rectangles if helpful).
• Measure sides/angles: take tape measurements (or GIS/plan values). For each triangle, use the
  Base × Height, Heron (3 sides), or two-sides + included angle method.
• Sum the parts: add up the areas of all triangles (and rectangles) to estimate the total land area.
• Convert units: present results in the unit needed (in², ft², m²). Common land units:
  1 acre = 43,560 ft²  •  1 m² ≈ 10.764 ft².

This triangle-decomposition method is widely used in surveying, mapping, and real estate for
land area calculator 4 sides scenarios and other complex footprints — a dependable, geometry-first workflow.

FAQs – Triangle Area Explained

Conclusion – Understanding the Triangle Area Calculator

The Triangle Area Calculator gives you everything you need to measure any triangle — whether you know
base and height, three sides, or an included angle.
It automatically applies Heron’s formula, base × height, or the sine rule depending on your inputs,
letting you switch methods instantly without extra math.

Whether you’re a geometry student, a builder checking floor dimensions, or a land surveyor estimating plots, this calculator delivers
instant accuracy in square inches, feet, or centimeters — no manual calculations required.
Combine it with other tools below to handle complex or irregular areas with precision.

• 🔹 Rectangle Area Calculator – for regular 4-sided shapes.
• 🔹 Missing Side Calculator – find unknown triangle or rectangle sides.
• 🔹 Square Inch Calculator – convert small surface areas quickly.
• 🔹 Sector Area Calculator – for circular and arc-based areas.

This free online triangle area calculator helps you learn, verify, and explore — all in one tool.
Try different inputs, compare units, and visualize how geometry translates into real-world measurements.