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Guides & explainers
Longer-form notes on the calculators we build — math, physics, finance, and the everyday numbers worth understanding.
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All guides
51 total
Finance
How CD Interest Is Calculated: APY, Compounding, and Penalties
CD interest follows A = P(1 + r/n)^(nt). Why banks quote APY and not the rate, how compounding frequency moves the total, and what breaking early costs.
Ugo Charles
Calculator
Gross vs Net: The Difference, With Dollar Examples
Gross is the total before deductions; net is what is left after deductions are subtracted. This guide explains gross vs net for pay, income, and profit with worked dollar examples and a quick comparison table.
Ugo Charles
Health
How Many Calories to Lose Weight: The Daily Number Explained
To lose weight, eat fewer calories than you burn each day. Find your maintenance calories with TDEE = BMR × activity, then subtract a deficit to set a daily target. This guide works the full chain end to end.
Ugo Charles
Calculator
How to Write a Check: A Step-by-Step Guide
Writing a check takes six fields: the date, the payee, the amount in numbers, the amount in words, an optional memo, and your signature. This guide walks every field with one worked example and shows exactly how to write the cents.
Ugo Charles
Health
Macros for Weight Loss: How to Set Protein, Carbs, and Fat
To set macros for weight loss, start from a calorie target below your TDEE, pick a split, then convert each percentage to grams: grams = calories × percent ÷ kcal per gram. Protein stays high on a cut.
Ugo Charles
Math
Slope-Intercept Form (y = mx + b): How to Find and Graph It
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. This guide shows how to find the equation from a graph, two points, or a point and slope, graph it, and convert standard form.
Ugo Charles
Calculator
What Is PEMDAS? The Order of Operations, Explained
PEMDAS is the order you do math operations: Parentheses, Exponents, Multiplication and Division, then Addition and Subtraction. This guide explains the rule, the left-to-right tie-breaker, the famous traps, and PEMDAS vs BODMAS.
Ugo Charles
Calculator
What Is the Mean? Definition, Formula, and How to Calculate It
The mean is the average of a set of numbers: add them all up and divide by how many there are. This guide shows the formula, a worked example, and how the mean differs from the median and mode.
Ugo Charles
Finance
The Compound Interest Formula: A = P(1 + r/n)^(nt), Explained
The compound interest formula is A = P(1 + r/n)ⁿᵗ, where P is the starting principal, r is the annual rate as a decimal, n is the number of times interest compounds per year, t is the number of years, and A is the final amount. This guide defines each variable, works a full example, and shows how compounding frequency changes the result.
Ugo Charles
Math
The Cylinder Volume Formula (V = πr²h): How It Works, With Examples
The volume of a cylinder is V = πr²h, where r is the radius of the circular base, h is the height, and π ≈ 3.14159. This guide shows why the formula works, walks through a full numerical example, and covers diameter inputs and unit conversions.
Ugo Charles
Physics
Density Formula: How to Find Density, Mass, or Volume
Use the density formula ρ = m/V, rearrange it for mass or volume, and check your units with worked examples.
Ugo Charles
Math
The Distance Formula: How to Find the Distance Between Two Points
The distance between two points is d = √((x₂−x₁)² + (y₂−y₁)²). It comes straight from the Pythagorean theorem: the horizontal and vertical gaps between the points are the two legs of a right triangle, and the distance is the hypotenuse.
Ugo Charles
Math
Exponent Rules (Laws of Exponents) With Examples
The laws of exponents let you multiply, divide, and nest powers without ever expanding them. Add the exponents to multiply, subtract to divide, multiply to raise a power to a power. This guide states each rule in one line and proves it with a worked example.
Ugo Charles
Health
How to Calculate BMI (Body Mass Index), With the Formula and Examples
BMI = weight in kilograms ÷ height in metres squared. If you measure in pounds and inches, BMI = 703 × weight (lb) ÷ height (in) squared. This guide shows both formulas worked end to end, the standard WHO category table, and what BMI can and cannot tell you.
Ugo Charles
Math
How to Calculate GPA (Grade Point Average), Step by Step
To calculate GPA, convert each letter grade to its point value on the 4.0 scale, multiply each by the course's credit hours to get quality points, sum those quality points, and divide by the total credit hours. This guide walks through the formula, a full worked example, weighted versus unweighted GPA, and cumulative GPA across semesters.
Ugo Charles
Math
The Pi Symbol (π): What It Means, Its Value, and How to Type It
π is the ratio of any circle's circumference to its diameter, a constant that equals about 3.14159. This guide explains what the symbol means, lists its digits and approximations, and shows how to type π on Windows, Mac, HTML, and LaTeX.
Ugo Charles
Math
The Quadratic Formula: How to Solve ax² + bx + c = 0
x = (−b ± √(b²−4ac)) / 2a solves any quadratic equation written in the form ax² + bx + c = 0. This guide works through the formula step by step, explains the discriminant, and covers when to use the formula instead of factoring.
Ugo Charles
Math
Scientific Notation: How to Write, Read, and Convert It
Scientific notation writes a number as a × 10ⁿ, where 1 ≤ |a| < 10 and n is an integer. This guide shows how to convert large and small numbers, how to read them back, and how to handle the E-notation calculators use.
Ugo Charles
Math
The Slope Formula: Rise Over Run, Explained With Examples
The slope formula is m = (y₂ − y₁) / (x₂ − x₁), which is just rise over run: the vertical change between two points divided by the horizontal change. This guide defines the points, works a full example, and covers all four slope cases.
Ugo Charles
Math
Square Root Symbol (√): What It Means, Its Name, and How to Type It
The √ symbol is the radical sign, and it asks one question: what number times itself gives the value sitting under it? So √9 = 3, because 3 × 3 = 9. This guide names every part of the symbol, lists the perfect squares, and shows how to type √ on Windows, Mac, in HTML, and in LaTeX.
Ugo Charles
Calculator
Celsius to Fahrenheit: Formula, Chart, and Everyday Conversions
To convert Celsius to Fahrenheit, multiply by 9/5 and add 32. This guide shows the formula with worked examples, a reference chart, and a quick mental math shortcut for when you don't have a calculator handy.
Ugo Charles
Calculator
Common Temperature Conversions: Room, Body, Weather, Cooking, and Baking
The temperatures you actually need to convert in daily life — room temperature, body temperature, oven settings, weather ranges, freezer and fridge. This guide converts each one in both directions with context.
Ugo Charles
Calculator
Fahrenheit to Celsius: Formula, Conversion Chart, and Worked Examples
To convert Fahrenheit to Celsius, subtract 32 and multiply by 5/9. This guide shows the formula with worked examples, a reference chart for common temperatures, and quick mental-math shortcuts.
Ugo Charles
Calculator
Pro Rata Rent in the UK: How to Calculate It (Landlord and Tenant Guide)
UK pro rata rent uses a slightly different set of conventions to US prorated rent. This guide covers the daily-rate, calendar-month, and 52-week methods, with worked examples for mid-month move-ins and assured shorthold tenancies.
Ugo Charles
Calculator
Determinant of a Matrix: Formula, Rules, and Worked 2×2 and 3×3 Examples
The determinant of a matrix is a single number that tells you whether the matrix is invertible and how it scales area or volume. This guide shows the 2×2 and 3×3 formulas with worked examples and the rules that save time.
Ugo Charles
Math
Dot Product of Two Vectors: Formula, Meaning + Examples
Learn the dot product formula for 2D, 3D, and n-dimensional vectors, what the sign means, how to find an angle, and where projections come from.
Ugo Charles
Calculator
Find the Product: Step-by-Step Examples for Whole Numbers, Fractions, and Decimals
"Find the product" just means "multiply." This guide walks through worked examples with whole numbers, fractions, decimals, and word problems so you can answer any "find the product" question on the spot.
Ugo Charles
Calculator
How to Calculate Prorated Rent: Formula, Examples, and Move-In / Move-Out Scenarios
Prorated rent is what you pay when you move in or out partway through a month. This guide shows the two main formulas (daily rate and banker's method), walks through move-in and move-out examples, and flags the edge cases landlords and tenants fight about.
Ugo Charles
Calculator
How to Find the Least Common Denominator (LCD): Step-by-Step Method
Finding the LCD of two or more fractions takes three steps: list multiples, find the smallest match, rewrite each fraction. This guide shows the method with worked examples, plus a prime-factorization shortcut for larger numbers.
Ugo Charles
Economics
How to Calculate Consumer Surplus
Calculate consumer surplus for one purchase or a demand curve, with the formula, worked examples, and common mistakes.
Ugo Charles
Calculator
How to Calculate Frequency: A Beginner’s Guide to Understanding Waves
Discover how to calculate frequency step by step using time periods, wavelength, and angular frequency. Perfect for beginners, this guide uses simple analogies and real-life examples to make frequency easy to understand.
Ugo Charles
Calculator
How to Calculate Percent Yield: A Friendly Beginner’s Guide
Learn how to calculate percent yield step-by-step using a simple formula. Perfect for beginners, this guide explains theoretical vs actual yield, provides easy examples, and shares common mistakes to avoid.
Ugo Charles
Calculator
How to Calculate Marginal Revenue: Formula and Worked Example
Marginal revenue is the extra money from selling one more unit. Here is the formula, a worked example, and the MR = MC rule that tells you when one more sale is worth making.
Ugo Charles
Finance
Marginal Cost Formula: How to Calculate It (With Examples)
Marginal cost is the change in total cost divided by the change in quantity. Formula, worked bakery and service examples, and how it drives pricing.
Ugo Charles
Finance
How to Calculate Cost of Goods Sold (COGS)
Calculate COGS from beginning inventory, purchases, and ending inventory, then use it to find gross profit and margin.
Ugo Charles
Statistics
How to Calculate Standard Deviation in Excel
Use STDEV.S or STDEV.P in Excel, choose the right one for your data, and check the result against a worked example.
Ugo Charles
Calculator
How to Calculate Range in Statistics (Beginner’s Guide with Real-Life Examples)
A friendly, beginner-focused guide to understanding and calculating range in statistics. Learn what range means, how to compute it, real-life applications, and common mistakes to avoid.
Ugo Charles
Calculator
How to Calculate Gross Profit: A Beginner’s Guide to Understanding Your Business Finances
A beginner-friendly guide that explains what gross profit is, how to calculate it, and why it’s essential for making smarter business decisions. No finance degree needed—just simple formulas, real-life examples, and tips to avoid costly mistakes.
Ugo Charles
Calculator
How to Calculate Cubic Feet (Even If You Hated Math in School)
Cubic feet might sound complicated, but it’s one of the most practical measurements you’ll ever use. Learn how to calculate it with simple steps, real-life examples, and beginner-friendly tips.
Ugo Charles
Chemistry
How to Calculate Theoretical Yield
Calculate theoretical yield from a balanced equation, molar masses, and the limiting reactant, then compare it with percent yield.
Ugo Charles
Math
How to Calculate Percent Error (Formula + Examples)
Calculate percent error with the absolute-error formula, worked examples, and the mistakes that change the answer.
Ugo Charles
Physics
How to Calculate Acceleration (Formula + Examples)
Calculate acceleration from starting velocity, final velocity, and time. Includes unit checks, negative acceleration, and worked examples.
Ugo Charles
Physics
How to Calculate Velocity (Formula, Direction + Examples)
Calculate velocity from displacement and time, keep direction in the answer, and avoid confusing velocity with speed.
Ugo Charles
Finance
How to Calculate Retained Earnings
Calculate retained earnings from beginning retained earnings, net income, and dividends, with examples and accounting checks.
Ugo Charles
Economics
How to Calculate Opportunity Cost
Calculate opportunity cost by comparing the next best option with the option you chose, using money, time, or output.
Ugo Charles
Math
How to Find a Square Root Without a Calculator
Estimate square roots by hand, then refine them with the Babylonian method or long-division style steps.
Ugo Charles
Math
Inner Product: Definition, Axioms + Examples
Learn what an inner product is, the axioms it must satisfy, and how dot products, weighted products, complex vectors, and functions fit the definition.
Ugo Charles
Calculator
What Does "Product" Mean in Math? Definition, Examples, and How to Find It
In math, the product is the answer you get when you multiply numbers. This guide defines the term, shows how to find the product of whole numbers, fractions, and decimals, and answers the most common questions teachers and parents ask.
Ugo Charles
Calculator
What Is a Midpoint Calculator (And Why You Might Actually Use One)?
Ever wondered how to find the exact middle between two places or points? A midpoint calculator does just that! Whether you’re meeting a friend halfway, solving a geometry problem, or designing something symmetrical, this guide breaks it all down with simple language and real-life examples.
Ugo Charles