Solve complex mathematical problems with our free, easy-to-use calculators for geometry, algebra, statistics, and more.
Calculate the area of various shapes and polygons.
Calculate the volume of 3D shapes like cubes, spheres, cylinders, and more.
Calculate the perimeter of various shapes and polygons.
Calculate the area, circumference, diameter from radius or other parameters.
Solve quadratic equations and find the roots or zeros.
Calculate percentages, increases, decreases, and differences.
Add, subtract, multiply, and divide fractions with step-by-step solutions.
Solve linear equations with step-by-step solutions.
Calculate central tendencies in a data set.
Calculate standard deviation, variance, and other statistical measures.
Calculate probability of events, combinations, and permutations.
Calculate z-scores and probabilities using the normal distribution.
Calculate angles, sides, area, and perimeter of triangles.
Calculate sine, cosine, tangent, and their inverses.
Solve right triangles using the Pythagorean theorem and trigonometry.
Convert between degrees, radians, and gradians.
Calculate derivatives of functions with step-by-step solutions.
Calculate definite and indefinite integrals with step-by-step solutions.
Calculate limits of functions with step-by-step solutions.
Calculate Taylor series expansions of functions around a point.
The area of a circle is calculated using the formula: Area = π × r², where r is the radius of the circle and π (pi) is approximately 3.14159. For example, if a circle has a radius of 5 units, its area would be: Area = 3.14159 × 5² = 3.14159 × 25 = 78.54 square units.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of squares of the other two sides. If we call the hypotenuse c and the other two sides a and b, the formula is: a² + b² = c². This fundamental theorem is used extensively in geometry, trigonometry, and many practical applications.
A quadratic equation in the form ax² + bx + c = 0 (where a ≠ 0) can be solved using the quadratic formula: x = [-b ± √(b² - 4ac)] / 2a. The ± symbol indicates that there are typically two solutions. The expression b² - 4ac is called the discriminant, which determines the nature of the roots (real and distinct, real and equal, or complex).
Mean, median, and mode are measures of central tendency in statistics. The mean is the average of all values (sum divided by count). The median is the middle value when data is arranged in order (or average of two middle values). The mode is the most frequently occurring value. Each provides different insights about a data set and is useful in different contexts.
To convert from degrees to radians, multiply the degree value by π/180. For example, 90° = 90 × (π/180) = π/2 radians. To convert from radians to degrees, multiply the radian value by 180/π. For example, π radians = π × (180/π) = 180°. Remember that a full circle is 360° or 2π radians.
Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that values are spread out over a wider range. It's important in statistics because it helps understand the distribution of data and is used in many statistical tests, quality control applications, and financial analyses.
The volume of a sphere is calculated using the formula: V = (4/3) × π × r³, where r is the radius of the sphere. For example, if a sphere has a radius of 3 units, its volume would be: V = (4/3) × 3.14159 × 3³ = (4/3) × 3.14159 × 27 ≈ 113.1 cubic units.
A derivative represents the rate of change of a function with respect to one of its variables. Geometrically, it represents the slope of the tangent line to the graph of the function at a specific point. Derivatives are fundamental to calculus and have numerous applications in physics, engineering, economics, and other fields where measuring rates of change is important.
To find the equation of a line from two points (x₁, y₁) and (x₂, y₂), first calculate the slope: m = (y₂ - y₁) / (x₂ - x₁). Then use the point-slope form: y - y₁ = m(x - x₁). This can be rearranged to the slope-intercept form: y = mx + b, where b = y₁ - mx₁ is the y-intercept.
The six basic trigonometric functions are sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). For a right triangle, if θ is an angle, then sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent. The other functions are reciprocals of these: csc(θ) = 1/sin(θ), sec(θ) = 1/cos(θ), and cot(θ) = 1/tan(θ).