Your all-in-one
Math workspace.

Start with the expression inside parentheses, then evaluate powers and roots, multiplication and division, and finally addition and subtraction. Use explicit parentheses whenever an expression could be interpreted in more than one way. For trigonometry, confirm whether your angle is in degrees or radians before calculating sin, cos, or tan.

The mean is the sum of observations divided by the number of observations. Variance measures average squared distance from the mean. Population variance divides by n; sample variance divides by n − 1. Standard deviation is the square root of variance and is expressed in the same units as the original data.

To find a percentage of an amount, multiply the amount by the percentage divided by 100. A flat tax estimate is taxable amount multiplied by the tax rate; real tax systems may include thresholds, deductions, and other rules. For a fixed-rate amortizing loan, the monthly payment depends on principal, monthly interest rate, and number of monthly payments. Always compare fees and the full repayment total.

For ax² + bx + c = 0, the discriminant is D = b² − 4ac. If D is positive, there are two distinct real roots; if zero, there is one repeated real root; if negative, the roots are complex. The quadratic formula is x = (−b ± √D)/(2a), where a must not be zero.