Learn the math

Short tutorials that unpack the formulas behind each tool.

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Fitness · 5 min

How to Calculate BMI

Body mass index (BMI) is a screening ratio: body mass divided by the square of height. This tutorial walks through the SI formula, a 70 kg / 1.75 m worked example, and WHO adult category bands you can try with sliders. BMI is not a diagnosis of health, body fat, or disease.

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Fitness · 5 min

How to Calculate BMR

Basal metabolic rate (BMR) estimates the calories your body uses at rest. This tutorial walks through the Mifflin–St Jeor formulas, a 70 kg / 175 cm / age 30 worked example, and a playground that substitutes your numbers. BMR is an estimate of resting energy, not a meal plan or a medical assessment.

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Physics · 8 min

How to Calculate Angular Resolution with the Rayleigh Criterion

Two point sources are just resolved when the first dark ring of one Airy pattern sits on the peak of the other. For a circular aperture that split is θ = 1.22 λ / D. This tutorial works 550 nm through a 10 cm opening to 6.71×10⁻⁶ rad ≈ 1.38″, the same defaults as the Angular Resolution Calculator.

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Geometry · 7 min

How to Find the Centroid of a Right Triangle at (b/3, h/3)

If a right triangle has its right angle at the origin, the centroid is not a mystery point you have to construct from scratch. From that right-angle vertex, G = (b/3, h/3): one-third of the way along the base and one-third of the way up the height. This tutorial derives that shortcut from the three-vertex average, works b = 6 and h = 4, and opens the same points in the Centroid of a Triangle Calculator.

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Personal Finance · 5 min

How to Calculate Compound Interest

Compound interest reinvests earned interest into the balance, so later periods earn interest on interest. This tutorial walks through A = P(1 + r/m)^{mt}, a $5,000 / 4% / 10-year monthly worked example, and a playground that compares compound growth with simple interest. Figures are illustrative; fees and taxes are omitted.

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Math · 10 min

How to Calculate Your GPA for Free Online

You can calculate a college GPA for free on this site without creating an account or uploading a transcript. This walkthrough is for university credit hours on a 4.0 scale: gather what your registrar actually uses, run one term in the Semester GPA Calculator, convert assignment percents when you still have scores instead of letters, check whether a course goal is still reachable on the final, and plan a cumulative target. The pages are teaching checks, not an official record.

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Math · 5 min

How to Calculate a Percentage

A percentage compares a part to a whole on a scale of 100. This tutorial walks through the three problems the Percentage Calculator solves: what is P% of X, X as a percent of Y, and percent change from A to B. The worked example uses the same 15% of 80 defaults as the calculator.

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Geometry · 8 min

How to Calculate Surface Area to Volume Ratio

Surface-to-volume ratio is the outside divided by the inside: S/V. This tutorial uses the three solids the Surface Area to Volume Ratio Calculator actually takes — sphere, cube, and rectangular box — works the default sphere of radius 3 to S/V = 1, and lets you switch shapes in a playground.

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