Essential Math, Percentage, and Geometry Calculation Guide
Quick formulas for percentages, averages, geometric shapes, and algebraic ratios.
📚 Overview
Mathematics is the language of problem solving. Whether you need to determine percentage markdowns, compute geometric volumes, or calculate weighted grade averages, having reliable mathematical equations at your fingertips makes complex problems simple and error-free.
📐 Percentage Change & Area / Volume Equations
A positive result represents an increase, while a negative result represents a decrease. Geometric formulas include Circle Area = πr² and Triangle Area = 0.5 × base × height.
🔢 Worked Example
Scenario: An online product price changed from $80 down to $60 during a seasonal sale.
- Old Value: $80
- New Value: $60
- Difference = 60 - 80 = -20
- Divide by original = -20 / 80 = -0.25
- Multiply by 100 = -0.25 × 100% = -25%
💡 Pro Tips
- A 50% decrease followed by a 50% increase does not return to the original number ($100 → $50 → $75).
- When calculating averages with outliers, consider median values instead of arithmetic mean.
- Always follow the standard order of operations: Parentheses, Exponents, Multiplication & Division, Addition & Subtraction (PEMDAS).
- Use our geometry tools to calculate perimeter, area, and volume with exact mathematical constants.
🧮 Math Calculators (26)
Put the formulas above into practice with these free tools:
Find X percent of any number.
Increase or decrease between two values.
Mean, median, and sum of a list of numbers.
Hypotenuse and area of a right triangle.
Area, circumference, and diameter from the radius.
Area, perimeter, and diagonal of a rectangle.
Real roots of ax² + bx + c = 0.
Greatest common divisor and least common multiple.
❓ Frequently Asked Questions
What is the difference between mean, median, and mode?
Mean is the sum of values divided by count; median is the middle value in an ordered set; mode is the most frequently occurring value.
How do I calculate percentage of a number quickly?
Multiply the number by the percentage written as a decimal (e.g. 15% of $80 is 80 × 0.15 = $12).
What is the Pythagorean theorem?
In any right-angled triangle, a² + b² = c², where c is the hypotenuse opposite the 90-degree right angle.