Comprehensive tools for plane geometry, solid geometry, coordinate geometry, transformations, curves, and surfaces. Get step-by-step solutions for all your geometry problems.
Our comprehensive geometry calculator provides powerful tools for solving a wide range of geometric problems. Whether you're working with 2D shapes like triangles and circles, 3D objects like spheres and polyhedra, or need to perform coordinate geometry calculations and geometric transformations, our calculator has you covered. Get accurate results with step-by-step solutions to enhance your understanding of geometric concepts.
Calculate properties of 2D geometric figures such as triangles, circles, rectangles, and polygons.
Area (using base and height): $$A = \frac{1}{2} \times b \times h$$
Area (using sides - Heron's formula): $$A = \sqrt{s(s-a)(s-b)(s-c)}$$ where $$s = \frac{a+b+c}{2}$$
Perimeter: $$P = a + b + c$$
Area: $$A = \pi r^2$$
Circumference: $$C = 2\pi r$$
Diameter: $$d = 2r$$
Area: $$A = l \times w$$
Perimeter: $$P = 2(l + w)$$
Diagonal: $$d = \sqrt{l^2 + w^2}$$
Area: $$A = \frac{1}{4} \times n \times s^2 \times \cot(\frac{\pi}{n})$$
Perimeter: $$P = n \times s$$
Interior angle: $$\theta = \frac{(n-2) \times 180°}{n}$$
Calculate properties of 3D geometric figures such as cubes, spheres, cylinders, cones, and polyhedra.
Volume: $$V = s^3$$
Surface Area: $$A = 6s^2$$
Diagonal: $$d = s\sqrt{3}$$
Volume: $$V = \frac{4}{3}\pi r^3$$
Surface Area: $$A = 4\pi r^2$$
Volume: $$V = \pi r^2 h$$
Surface Area: $$A = 2\pi r^2 + 2\pi r h$$
Volume: $$V = \frac{1}{3}\pi r^2 h$$
Surface Area: $$A = \pi r^2 + \pi r l$$ where $$l = \sqrt{r^2 + h^2}$$
Specify geometric figures by coordinates or algebraic equations, and calculate properties such as distance, midpoint, slope, and more.
$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$
$$M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$$
$$m = \frac{y_2 - y_1}{x_2 - x_1}$$
Point-Slope Form: $$y - y_1 = m(x - x_1)$$
Slope-Intercept Form: $$y = mx + b$$
General Form: $$Ax + By + C = 0$$
Visualize and compute properties for different kinds of geometric transformations such as translations, rotations, reflections, and scaling.
$$T(x, y) = (x + h, y + k)$$
Matrix form: $$\begin{pmatrix} x' \\ y' \\ 1 \end{pmatrix} = \begin{pmatrix} 1 & 0 & h \\ 0 & 1 & k \\ 0 & 0 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \\ 1 \end{pmatrix}$$
Around origin: $$R(x, y) = (x\cos\theta - y\sin\theta, x\sin\theta + y\cos\theta)$$
Matrix form: $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$
Across x-axis: $$R_x(x, y) = (x, -y)$$
Across y-axis: $$R_y(x, y) = (-x, y)$$
Across line y = x: $$R_{y=x}(x, y) = (y, x)$$
$$S(x, y) = (sx, sy)$$
Matrix form: $$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} s_x & 0 \\ 0 & s_y \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}$$
Visualize and compute properties of curves and surfaces in 2D and 3D space.
Standard Form: $$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$$
Area: $$A = \pi ab$$
Perimeter (Approximation): $$P \approx 2\pi\sqrt{\frac{a^2+b^2}{2}}$$
Eccentricity: $$e = \sqrt{1 - \frac{b^2}{a^2}}$$ (where $$a > b$$)
Standard Form: $$y = a(x-h)^2 + k$$
Focus: $$F = (h, k + \frac{1}{4a})$$
Directrix: $$y = k - \frac{1}{4a}$$
Standard Form: $$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2} = 1$$
Asymptotes: $$y - k = \pm\frac{b}{a}(x - h)$$
Eccentricity: $$e = \sqrt{1 + \frac{b^2}{a^2}}$$
Equation: $$(x-x_0)^2 + (y-y_0)^2 + (z-z_0)^2 = r^2$$
Volume: $$V = \frac{4}{3}\pi r^3$$
Surface Area: $$A = 4\pi r^2$$
Find the distance between points (2, 3) and (5, 7) in the coordinate plane.
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