Geometry Calculator - Calculate Area, Volume, Surface Area and More
Advertisement
Geometry Calculator
Calculate area, perimeter, volume, surface area and more with step-by-step solutions
Area Calculator
Volume Calculator
Surface Area
Angles Calculator
Area Calculator
Calculate the area of various geometric shapes. Select a shape and enter the required dimensions.
Square
Rectangle
Triangle
Circle
Trapezoid
Area Calculation Results
0.0
Formula: Area = a²
Calculation Steps:
1. Identify the shape: Square
2. Apply the formula: Area = side × side
3. Substitute values: Area = 5 × 5
4. Calculate: Area = 25 square units
Shape Properties
Side length: 5 units
Perimeter: 20 units
Related Calculations
Diagonal: 7.07 units
Inscribed circle area: 19.63 sq units
Volume Calculator
Calculate the volume of various 3D shapes. Select a shape and enter the required dimensions.
Cube
Sphere
Cylinder
Cone
Pyramid
Volume Calculation Results
0.0
Formula: Volume = a³
Calculation Steps:
1. Identify the shape: Cube
2. Apply the formula: Volume = side × side × side
3. Substitute values: Volume = 5 × 5 × 5
4. Calculate: Volume = 125 cubic units
Shape Properties
Side length: 5 units
Surface Area: 150 sq units
Related Calculations
Space Diagonal: 8.66 units
Weight (if water): 125 kg
Surface Area Calculator
Calculate the surface area of various 3D shapes. Select a shape and enter the required dimensions.
Cube
Sphere
Cylinder
Cone
Pyramid
Surface Area Calculation Results
0.0
Formula: Surface Area = 6a²
Calculation Steps:
1. Identify the shape: Cube
2. Apply the formula: Surface Area = 6 × side × side
3. Substitute values: Surface Area = 6 × 5 × 5
4. Calculate: Surface Area = 150 square units
Shape Properties
Side length: 5 units
Volume: 125 cubic units
Related Calculations
Area per face: 25 sq units
Surface to Volume Ratio: 1.2
Angles Calculator
Calculate angles in various geometric shapes and solve trigonometric problems.
Triangle
Right Triangle
Polygon
Circle
Trigonometry
Angles Calculation Results
0.0°
Formula: Sum of angles = (n-2) × 180°
Calculation Steps:
1. Identify the shape: Triangle
2. Apply the formula: Sum of angles = 180°
3. Substitute values: 45° + 45° + 90° = 180°
4. Calculate: Missing angle = 90°
Angle Properties
Type: Right triangle
Complementary angles: 45°
Related Calculations
In radians: 1.57 rad
sin(90°) = 1, cos(90°) = 0
Understanding Geometry Calculations
Geometry is a branch of mathematics that deals with shapes, sizes, relative positions of figures, and properties of space. Calculators for geometry help students, teachers, engineers, and designers quickly solve geometric problems and verify their manual calculations.
Key Geometry Concepts
Important concepts in geometry include:
Area: The amount of space inside a 2D shape
Perimeter: The distance around a 2D shape
Volume: The amount of space occupied by a 3D object
Surface Area: The total area of all surfaces of a 3D object
Angles: The measure of rotation between two intersecting lines
Common Formulas
Some of the most commonly used geometry formulas include:
Square Area: A = a² (where a is side length)
Circle Area: A = πr² (where r is radius)
Triangle Area: A = ½bh (where b is base, h is height)
Cube Volume: V = a³
Sphere Volume: V = (4/3)πr³
Cylinder Surface Area: A = 2πrh + 2πr²
Applications of Geometry
Geometry has practical applications in many fields:
Architecture and Construction: Designing buildings and structures
Engineering: Creating mechanical parts and systems
Computer Graphics: Rendering 3D models and animations
Navigation: Calculating distances and routes
Art and Design: Creating visually appealing compositions
Understanding geometric principles and having access to reliable calculation tools is essential for professionals and students in these fields.
Frequently Asked Questions About Geometry Calculations
What is the difference between area and perimeter?
Area measures the space inside a 2D shape, while perimeter measures the distance around the outside of the shape.
How do I calculate the volume of an irregular shape?
For irregular shapes, volume can often be calculated using water displacement methods or by breaking the shape down into smaller regular shapes and summing their volumes.
What is Pythagoras' theorem?
Pythagoras' theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides: a² + b² = c².
How do I convert between degrees and radians?
To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π.
What is the formula for the area of a circle?
The area of a circle is calculated using the formula A = πr², where r is the radius of the circle.
How do I calculate the surface area of a cylinder?
The surface area of a cylinder is calculated as 2πrh + 2πr², where r is the radius and h is the height.