Formula Derivation Tool

A Formula Derivation Tool is an educational resource that shows the step-by-step mathematical process of how formulas are derived from first principles. Unlike memorizing formulas, understanding derivations helps students build conceptual clarity, perform better in exams (especially board exams in Pakistan, India, and other countries), and apply formulas correctly in different contexts. Our tool uses a pure mathematical rule-based engine to generate exam-ready derivation steps—no AI or API required.

Our Formula Derivation Tool covers 6 major subjects: Physics (equations of motion, Newton's laws, kinetic & potential energy, E=mc²), Mathematics (quadratic formula, binomial theorem, Pythagorean theorem, circle area), Electrical Engineering (Ohm's Law, power equations, series/parallel circuits), Chemistry (ideal gas law, pH formulas), Statistics (mean, variance, standard deviation), and Economics. Each subject is organized into chapters with searchable formulas indexed by variables, units, topic, and difficulty level.

The Given-To-Prove mode simulates the exact format used in board exams and university papers. You enter a "Given" equation (e.g., a = (v-u)/t) and a "Prove That" equation (e.g., v = u + at). The tool then generates a step-by-step proof showing each algebraic manipulation with explanations, ending with "Hence Proved" (Q.E.D.). This format is ideal for practicing exam-style mathematical proofs and understanding algebraic transformations.

The Rearrangement mode allows you to solve any formula for a specific variable. Enter an equation (e.g., s = ut + ½at²), then select the variable you want to isolate (e.g., "a" for acceleration). The tool applies step-by-step algebraic operations—adding/subtracting terms, multiplying/dividing both sides, taking roots—to isolate your target variable. Each step is explained, making it perfect for understanding how to manipulate physics and math formulas on exams.

Learning Mode shows detailed explanations for each step, highlights applied laws/theorems, and provides extra context—ideal for understanding concepts and building intuition. Exam Mode provides clean, board-approved steps without extra explanation—exactly what you would write in an exam answer. Toggle between modes based on whether you're studying to understand (Learning) or practicing exam writing (Exam).

Yes! While we provide an extensive database of pre-defined formulas with step-by-step derivations, you can also enter any custom equation (e.g., "P = VI" or "F = ma") in the Custom Equation input field. The tool will parse your equation, identify variables, and allow you to use the Rearrangement mode to solve for any variable. This makes the tool versatile for formulas not yet in our database.

Export your derivations in multiple formats: PDF (print-ready document for homework submissions), Plain Text (quick copy-paste for notes), LaTeX (for academic papers and technical documents), and Exam Notes (structured Given/Required/Formula/Answer format). You can also copy derivations to clipboard with one click. All exports are generated locally—no server upload required.

Yes! When you enable the "Show Laws" option, each derivation step displays the underlying law, theorem, or principle being applied—such as Newton's Second Law, Conservation of Energy, Work-Energy Theorem, or Completing the Square. This helps you understand not just the mathematical manipulation but the physical or mathematical reasoning behind each step, which is crucial for conceptual exams.

The Formula Explorer is a browsable gallery of all formulas in our database. Filter by subject (Physics, Math, etc.), difficulty level (Easy, Medium, Hard), or search by formula name, equation, or variables. Each card shows the formula equation, subject, chapter, and difficulty. Click any card to instantly view its complete step-by-step derivation. It's a powerful way to explore and learn formulas beyond your immediate need.

100% Free & Offline. Our Formula Derivation Tool is completely free with no registration required. All derivations are generated using a client-side rule-based math engine—no AI, no API calls, no server processing. Once the page loads, you can disconnect from the internet and continue using all features. Your equations and derivations are never uploaded anywhere, making it perfectly safe for sensitive academic work and ideal for use in areas with limited connectivity.