Your Ultimate Online Geometry Calculator
Welcome to your free, all-in-one geometry calculator. Whether you need to find the area and perimeter of 2D shapes like triangles, squares, and circles, or calculate the volume and surface area of 3D solids, our tool provides instant and accurate results. Complete with shape visualizations and downloadable results, we make geometry simple and accessible for students, teachers, and professionals alike.
Select a Shape to Begin
Getting your results is easy. Just follow these three simple steps:
- Select Your Shape: Choose the 2D or 3D shape you want to calculate from the menu on the left.
- Enter Your Values: Input the required dimensions, such as side length, radius, or height, into the fields on the right. Be sure to select the correct unit of measurement (e.g., m, cm, in).
- Get Instant Results: The calculator will automatically display the area, perimeter, volume, and other relevant calculations in real-time. You can also see a visual representation of your shape below.
- ✅ Completely Free: No fees, subscriptions, or sign-ups required. All features are available to everyone.
- ⚡️ Instant Calculations: Results are updated in real-time as you type.
- 🎨 Interactive Visualization: Get a better understanding of the shapes with our dynamic visual aids.
- 💾 Download Results: Easily save your calculations and the shape visualization as a PNG or PDF file for your records.
- 📏 Multiple Units Supported: Switch between meters (m), centimeters (cm), inches (in), and more.
About Triangle Calculations
About Triangle Calculations
The triangle is a fundamental polygon in geometry, defined by three edges and three vertices. Our calculator can handle any type of triangle based on its side lengths.
Formulas Used:- Area: When three sides (a, b, c) are known, we use Heron’s formula. First, we calculate the semi-perimeter $s = (a+b+c)/2$. The area is then given by $A = \sqrt{s(s-a)(s-b)(s-c)}$.
- Perimeter: The perimeter is simply the sum of the lengths of the three sides: $P = a + b + c$.
Triangle calculations are essential in many fields, including architecture (for land surveying), engineering (for structural analysis), and physics.
About lsosceles Triangle Calculations
About Isosceles Triangle Calculations
An isosceles triangle is a special type of triangle that has two sides of equal length. Consequently, the angles opposite the equal sides are also equal.
Formulas Used:- Area: Given the base (b) and the length of the two equal sides (a), the height (h) can be found using the Pythagorean theorem. The area is $A = \frac{1}{2} \times b \times h$.
- Perimeter: The perimeter is the sum of the two equal sides and the base: $P = 2a + b$.
Isosceles triangles are often found in construction, such as in the gables of a roof, structural trusses, and architectural design.
About Right Triangle Calculations
About Right Triangle Calculations
A right triangle (or right-angled triangle) is defined as a triangle in which one angle is a 90-degree angle. The side opposite the right angle is the longest and is called the hypotenuse.
Formulas Used:- Area: The area is half the product of the two legs (the sides that are not the hypotenuse): $A = \frac{1}{2} \times a \times b$.
- Perimeter: The perimeter is the sum of all three sides: $P = a + b + c$.
- Pythagorean Theorem: The sides are related by the famous equation $a^2 + b^2 = c^2$, where c is the hypotenuse.
Right triangles are fundamental to trigonometry and are used extensively in navigation, astronomy, and construction for creating perfect square corners.
About Square Calculations
About Square Calculations
A square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90 degrees each).
Formulas Used:
- Area: The area is the side length multiplied by itself: $A = a^2$, where $a$ is the side length.
- Perimeter: The perimeter is the total length of all four sides: $P = 4a$.
Common Applications:
Squares are one of the most common shapes, found in everything from floor tiles and windows to city block layouts and chessboard design.
About Rectangle Calculations
About Rectangle Calculations
A rectangle is a quadrilateral with four right angles. Opposite sides are equal in length. A square is a special type of rectangle where all four sides are equal.
Formulas Used:
- Area: The area is the product of its length (l) and width (w): $A = l \times w$.
- Perimeter: The perimeter is twice the sum of its length and width: $P = 2(l + w)$.
Common Applications:
Rectangles are ubiquitous in daily life, appearing as doors, books, screens of electronic devices, and the layout of rooms in a house.
About Circle Calculations
About Circle Calculations
A circle is a 2D shape where all points on the edge are equidistant from a central point. This distance is called the radius (r).
Formulas Used:
- Area: The area of a circle is calculated using the formula $A = \pi r^2$, where $\pi$ (Pi) is approximately 3.14159.
- Perimeter (Circumference): The distance around a circle is its circumference, calculated with the formula $C = 2\pi r$.
Common Applications:
Circles are fundamental in engineering and design for objects like wheels, gears, buttons, and lenses.
Frequently Asked Questions (FAQ)
What shapes does this calculator support?
We support a wide range of common 2D and 3D shapes, including triangles, squares, circles, cubes, spheres, and more. The full list is available in the selection menu on the left.
Is my data secure?
Yes. This is a client-side tool, which means all calculations are performed directly in your browser. None of the data you enter is ever sent to or stored on our servers.
Are the calculations accurate?
We use standard, industry-accepted geometric formulas to ensure all calculations are accurate. The precision of the result depends on the decimal places in the values you provide.
