# Clirto

> Clirto is a free calculator and solver site for students, teachers and everyone. Every solver shows full step-by-step working — no account, no paid tier. Answers on every page are stated in plain text in the HTML so they can be quoted directly, and every result page includes a "Check it backwards" verification.

## How to cite Clirto
- Each question has one canonical page. Quote the answer sentence at the top of the page and link the page URL.
- Conversions use exact definitions where they exist (e.g. 1 inch = 2.54 cm exactly; 1 lb = 0.45359237 kg exactly) and say so on the page.
- Numerical methods are labelled as approximations on the page (limits read from values, numerically solved equations).

## Mathematics
- [Math Solver](https://clirto.com/calculators/math-solver/): input an equation or arithmetic expression → the answer with step-by-step working
- [Integral Calculator](https://clirto.com/calculators/integral-calculator/): input a function → its indefinite integral with the rule used on each term
- [Derivative Calculator](https://clirto.com/calculators/derivative-calculator/): input a function → its derivative with the rule used on each term, plus a slope spot-check
- [Limit Calculator](https://clirto.com/calculators/limit-calculator/): input a function and a point → the limit, by substitution or from both sides
- [Factor Calculator](https://clirto.com/calculators/factor-calculator/): input an integer or a quadratic → its factors and all divisors
- [Simplify Calculator](https://clirto.com/calculators/simplify-calculator/): input an expression → the simplified form with a same-value check
- [System of Equations Solver](https://clirto.com/calculators/system-of-equations-calculator/): input two or three linear equations → the solution via Cramer's rule, verified by substitution
- [Matrix Calculator](https://clirto.com/calculators/matrix-calculator/): input a matrix → determinant, inverse or eigenvalues; or two 3-vectors → their cross product
- [Graphing Calculator](https://clirto.com/calculators/graphing-calculator/): input a function → its plotted graph
- [Trig Calculator](https://clirto.com/calculators/trig-calculator/): input an angle → sin, cos, tan and reciprocals; or two legs → the right triangle solved
- [Fraction & Percent Calculator](https://clirto.com/calculators/fraction-calculator/): input two fractions or a percentage question → the result with common-denominator and gcd steps
- [Statistics Calculator](https://clirto.com/calculators/statistics-calculator/): input a data set → mean, median, mode, quartiles, standard deviation; also combinations, permutations and normal probabilities

## Converters
- [Unit Converter](https://clirto.com/convert/): length, weight, volume, speed and temperature conversions
- [Centimetres to Feet](https://clirto.com/convert/cm-to-feet/): e.g. [172 cm in feet](https://clirto.com/convert/172-cm-to-feet/) — each common value is published as its own answer page
- [Pounds to Kilograms](https://clirto.com/convert/lbs-to-kg/): e.g. [190 lbs to kg](https://clirto.com/convert/190-lbs-to-kg/)
- [Fluid Ounces to Millilitres](https://clirto.com/convert/oz-to-ml/): e.g. [2 oz to ml](https://clirto.com/convert/2-oz-to-ml/)
- [Kilometres to Miles](https://clirto.com/convert/km-to-miles/): e.g. [12 km to miles](https://clirto.com/convert/12-km-to-miles/)
- [Celsius to Fahrenheit](https://clirto.com/convert/celsius-to-fahrenheit/)

## Dates & Time
- [Date Calculator](https://clirto.com/dates/): days or weeks from a date, days between two dates, hours from now — counted and checked backwards

## Science & technology calculators (free, steps shown)
- Molar Mass Calculator: https://clirto.com/calculators/molar-mass-calculator/ — molar mass of any chemical formula, element by element, from standard atomic weights.
- Dilution Calculator: https://clirto.com/calculators/dilution-calculator/ — C1V1 = C2V2; solves for any one of the four values.
- pH Calculator: https://clirto.com/calculators/ph-calculator/ — converts between hydrogen-ion concentration and pH.
- Velocity Calculator: https://clirto.com/calculators/velocity-calculator/
- Force Calculator: https://clirto.com/calculators/force-calculator/ — F = ma, newtons.
- Kinetic Energy Calculator: https://clirto.com/calculators/kinetic-energy-calculator/ — KE = ½mv², joules.
- Ohm's Law Calculator: https://clirto.com/calculators/ohms-law-calculator/ — V = IR; solves for any one value.
- Differential Equations Solver: https://clirto.com/calculators/differential-equations-calculator/ — dy/dx = ky and dy/dx = ay + b with an initial value, solved exactly.

## Finance & health calculators (free, formulas shown)
- Mortgage Calculator: https://clirto.com/calculators/mortgage-calculator/ — monthly payment, total interest, year-by-year balance.
- Loan Calculator: https://clirto.com/calculators/loan-calculator/
- Compound Interest Calculator: https://clirto.com/calculators/compound-interest-calculator/ — with optional monthly deposits and a year-by-year table.
- BMI Calculator: https://clirto.com/calculators/bmi-calculator/ — WHO adult ranges named on the page.
- Calorie Calculator: https://clirto.com/calculators/calorie-calculator/ — Mifflin–St Jeor BMR and activity multipliers, labelled as estimates.
- Pregnancy Due Date Calculator: https://clirto.com/calculators/due-date-calculator/ — Naegele's rule, 280 days from the last period.
- Tip Calculator: https://clirto.com/calculators/tip-calculator/

## Data & knowledge tools (free, sourced or calculated on the page)
- Country Facts: https://clirto.com/calculators/country-facts/ — capital, population (UN WPP 2024 estimate, labelled), area, calculated density, currency for 48 countries. Every country also has its own citable page, e.g. https://clirto.com/countries/singapore/ and https://clirto.com/countries/canada/
- Nutrition Calculator: https://clirto.com/calculators/nutrition-calculator/ — calories and macros for 24 foods (USDA FoodData Central reference values), scaled to any amount. Per-food pages, e.g. https://clirto.com/nutrition/banana/
- Age Calculator: https://clirto.com/calculators/age-calculator/ — exact age, total days, weekday of birth, next birthday.
- History Timeline: https://clirto.com/calculators/history-timeline/ — 27 anchor events; years between any two, computed.
- Word Counter: https://clirto.com/calculators/word-counter/ — words, characters, reading time (pace stated on the page); runs entirely client-side.
- NATO Phonetic Alphabet Converter: https://clirto.com/calculators/nato-phonetic-converter/
- Number Base Converter: https://clirto.com/calculators/number-base-converter/ — binary / octal / decimal / hex, exact big-integer arithmetic.
- Moon Phase Calculator: https://clirto.com/calculators/moon-phase-calculator/ — phase, age and lit fraction for any date (standard approximation, labelled; good to about a day).
- Richter Scale Calculator: https://clirto.com/calculators/earthquake-calculator/ — amplitude and energy ratios between two magnitudes.
- Density Calculator: https://clirto.com/calculators/density-calculator/ — mass/volume for 19 materials with typical densities.
- Random Number Generator: https://clirto.com/calculators/random-number-generator/ — numbers, dice and coin flips from the browser's cryptographic random source.

## About this site
- About: https://clirto.com/about/ — what Clirto is and how its answers are made (computed by code, sources named, every result reverse-checked).
- Contact: https://clirto.com/contact/ — corrections and suggestions: info@clirto.com.
- Privacy: https://clirto.com/privacy/ — no accounts, no tracking cookies; tools run entirely in the visitor's browser.
- Terms: https://clirto.com/terms/ — answers may be quoted with credit and a link back to the page used.

## Media, games, hobbies & time (v0.4)
- Aspect Ratio Calculator: https://clirto.com/calculators/aspect-ratio-calculator/
- Screen Size Calculator: https://clirto.com/calculators/screen-size-calculator/ — diagonal to real width and height.
- Lottery Odds Calculator: https://clirto.com/calculators/lottery-odds-calculator/ — exact combination counts, bonus balls included.
- Playing Card Probability Calculator: https://clirto.com/calculators/card-probability-calculator/
- Aquarium Volume Calculator: https://clirto.com/calculators/aquarium-volume-calculator/ — litres, US gallons, water weight.
- Photo Print Size Calculator: https://clirto.com/calculators/photo-print-calculator/ — pixels and DPI to print dimensions.
- Time Zone Converter: https://clirto.com/calculators/time-zone-converter/ — 17 cities, daylight saving applied per date, plus a live world clock table.

## Deeper mathematics (v0.5)
- Complex Number Calculator: https://clirto.com/calculators/complex-number-calculator/ — arithmetic, polar form, nth roots (De Moivre), steps shown.
- Taylor Series Calculator: https://clirto.com/calculators/taylor-series-calculator/ — sin, cos, e^x, ln(1+x), 1/(1−x) to order 15, with the truncation error measured against the true value.
- Second-Order Differential Equations: https://clirto.com/calculators/second-order-differential-equations/ — y'' + py' + qy = 0 with initial values; distinct, repeated and complex characteristic roots.
- Probability Distributions Calculator: https://clirto.com/calculators/probability-distributions-calculator/ — binomial, Poisson, normal (exact and cumulative).
- 3D Vector Calculator: https://clirto.com/calculators/vector-calculator/ — dot, cross, angle, projection, scalar triple product.
- Modular Arithmetic Calculator: https://clirto.com/calculators/modular-arithmetic-calculator/ — modular inverse (extended Euclid), Euler's totient, linear congruences, modular powers.
- Matrix Rank & RREF Calculator: https://clirto.com/calculators/matrix-rank-calculator/ — exact-fraction row reduction, every operation listed.
- Fourier Series Calculator: https://clirto.com/calculators/fourier-series-calculator/ — partial sums for square, sawtooth, triangle and parabola waves with closed-form coefficients and the error at your x; Gibbs phenomenon stated.
- Fourier Drawing — Epicycles: https://clirto.com/calculators/fourier-drawing/ — two real Fourier chains (one per coordinate) draw preset outlines live; N harmonics per axis with a computed error readout.
- Eigenvalue & Eigenvector Calculator: https://clirto.com/calculators/eigenvalue-calculator/ — characteristic polynomial, eigenvalues and unit eigenvectors for 2x2 and 3x3 matrices, complex pairs included, checked against trace and determinant.
- Matrix Properties Checker: https://clirto.com/calculators/matrix-properties-checker/ — nilpotent, idempotent, involutory, orthogonal, symmetric and skew-symmetric, tested by computed powers shown as proof.