How-To Guides
Step-by-step guides that teach you how to perform calculations manually.
How to Check Divisibility Using Rules: Step-by-Step Guide
Learn to manually apply divisibility rules for numbers 2, 3, 4, 5, 6, 8, 9, 10. Understand formulas, examples, and common pitfalls.
Read guideHow to Determine if a Number is a Perfect Cube and Find its Cube Root: Step-by-Step Guide
Learn to manually check if an integer is a perfect cube and calculate its cube root using prime factorization and estimation. Includes examples and common pitfalls.
Read guideHow to Calculate Perfect Squares: Step-by-Step Guide
Learn to manually check if a number is a perfect square and find its integer square root using estimation and iterative testing. Includes examples and common pitfalls.
Read guideHow to Calculate Parabola Parameters: Step-by-Step Guide
Learn to manually calculate a parabola's focus, directrix, and latus rectum from its equation. Includes formulas, examples, and pitfalls.
Read guideHow to Calculate Eigenvalues of a 2x2 Matrix: Step-by-Step Guide
Learn to manually calculate eigenvalues of a 2x2 matrix. Step-by-step guide with formulas, a worked example, and common pitfalls for STEM professionals.
Read guideHow to Convert and Analyze Parametric Curves: Step-by-Step Guide
Learn to manually convert parametric equations to Cartesian form and analyze curves. Step-by-step guide with formulas, examples, and common pitfalls.
Read guideHow to Perform Modular Arithmetic: Step-by-Step Guide
Learn modular arithmetic with ease
Read guideHow to Calculate Complex Numbers: Step-by-Step Guide
Add, subtract, multiply, divide complex numbers manually
Read guideCubic Equation Solver: Step-by-Step Guide
Solve cubic equations manually
Read guideHow to Generate the Fibonacci Sequence and Golden Ratio: Step-by-Step Guide
Learn to manually generate Fibonacci sequences and approximate the Golden Ratio with this step-by-step guide, formulas, and examples.
Read guideHow to Calculate Taylor Series: Step-by-Step Guide
Learn to manually calculate Taylor series approximations for functions. Understand the formula, derivatives, and common pitfalls.
Read guideHow to Convert Between Polar and Cartesian Coordinates: Step-by-Step Guide
Master the conversion between Cartesian (x, y) and Polar (r, θ) coordinates. Learn formulas, manual calculation steps, common pitfalls, and unit considerations.
Read guideHow to Calculate Matrix Inverse: Step-by-Step Guide
Learn to manually calculate the inverse of 2x2 and 3x3 matrices. Step-by-step formulas, worked examples, common pitfalls, and when to use computational tools for accuracy.
Read guideHow to Calculate the Matrix Determinant: Step-by-Step Guide
Learn to manually calculate the determinant of 2x2 and 3x3 matrices using direct formulas and Sarrus's Rule. Includes examples and common pitfalls.
Read guideHow to Calculate the Vector Cross Product: Step-by-Step Guide
Learn to manually calculate the 3D vector cross product (A×B). Step-by-step guide covers the formula, a worked example, common pitfalls, and applications for engineers.
Read guideHow to Solve Quadratic Equations by Completing the Square: Step-by-Step Guide
Learn to solve quadratic equations by completing the square. Manual step-by-step guide with formulas, worked examples, and common pitfalls.
Read guideHow to Calculate Percent Error: Step-by-Step Guide
Learn to calculate percent error manually. Understand the formula, absolute error, and relative error with a worked example. Avoid common pitfalls.
Read guideHow to Calculate Percent Difference: Step-by-Step Guide
Learn to calculate the percent difference between two values manually. This guide covers the formula, a worked example, common pitfalls, and when to use a calculator.
Read guideHow to Calculate Percent Change: Step-by-Step Guide
Learn to manually calculate percent change between two values using a simple formula. Step-by-step guide with examples and common pitfalls.
Read guideHow to Calculate Binomial Products Using the FOIL Method: Step-by-Step Guide
Master the FOIL method to multiply two binomials. Learn the formula, step-by-step application, and worked examples for (a+b)(c+d) manually.
Read guideHow to Calculate Absolute Value: Step-by-Step Guide
Learn to calculate the absolute value of any number or expression manually. This guide includes the formula, worked examples, and common pitfalls.
Read guideHow to Calculate Logarithms: Step-by-Step Guide
Learn to manually calculate logarithms using their fundamental definition and the change of base formula. Includes step-by-step instructions, a worked example, and common pitfalls to avoid.
Read guideHow to Simplify Radicals and Calculate Roots: Step-by-Step Guide
Learn to simplify radical expressions and calculate roots manually. Understand the formula, prime factorization method, and common pitfalls with a worked example.
Read guideHow to Perform Complex Number Operations: A Step-by-Step Guide
Learn to manually add, subtract, multiply, divide, and find the modulus of complex numbers with formulas and examples.
Read guideHow to Calculate Decimal Rounding: Step-by-Step Guide
Learn to manually round decimals to any specified place. This guide covers the rules, provides a step-by-step example, and highlights common rounding pitfalls.
Read guideHow to Calculate the Reciprocal: Step-by-Step Guide
Learn to manually calculate the reciprocal (multiplicative inverse) of any number or fraction with formulas, examples, and pitfalls.
Read guideHow to Calculate Cube Root: Step-by-Step Guide
Learn to calculate the cube root of any number manually using the Newton-Raphson method. This guide covers the formula, worked examples, common pitfalls, and when to use a calculator for convenience.
Read guideHow to Calculate the Square Root: Step-by-Step Guide
Master square root calculation by hand using the Babylonian method. This guide provides formulas, a worked example, common pitfalls, and calculator usage tips for engineers.
Read guideHow to Calculate Exponents: Step-by-Step Guide
Learn to manually calculate exponents (powers) step-by-step. Understand the formula, worked examples, common pitfalls, and when to use a calculator.
Read guideHow to Calculate Roots Using the Quadratic Formula: Step-by-Step Guide
Learn to solve any quadratic equation ax²+bx+c=0 manually using the quadratic formula. Step-by-step guide with examples and common pitfalls.
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