Math & Algebra
Math & algebra tools are free online calculators that solve, simplify and explain everyday number problems — percentages, fractions, roots, exponents, geometry and sequences — for students, teachers and professionals.
Free arithmetic sequence calculator that finds the nth term and the sum of the first n terms from the first term, common difference and term number, with steps shown.
Free average calculator: enter a list of numbers to find the average (mean), sum, count, minimum, maximum and range instantly, with worked examples.
Convert any binary number to decimal instantly. Enter 0s and 1s and see the base-10 value, hex equivalent, and a clear place-value breakdown.
Calculate the area of a circle from its radius or diameter. Free circle area calculator that also returns the circumference and diameter with the formula shown.
Free circle calculator: enter any one of radius, diameter, circumference or area and instantly get the other three, with the exact formulas and worked examples shown.
Find the circumference of a circle from its radius, diameter or area. Free circumference calculator that also returns the diameter and area with the C = 2πr formula shown.
Find the critical points of any function f(x) and classify each as a local minimum, maximum, or inflection point. Enter a function, see f'(x), and get the points instantly.
Find the cube root of any number instantly. Enter a value to get its real cube root, see whether it is a perfect cube, and check the result by cubing.
Calculate the volume of a cylinder from its radius and height. Free cylinder volume calculator that also returns total surface area with the formula and steps shown.
Convert decimal numbers to binary instantly. Enter any whole number and see its base-2 form, hex equivalent, and the division-by-2 steps explained.
Convert any decimal to a fraction instantly. Enter a decimal to get the fraction in lowest terms, a mixed number, and the reducing steps explained.
Find the straight-line distance between two points on a coordinate plane. Free distance formula calculator with step-by-step working using the Pythagorean theorem.
Free exponent calculator that raises any base to a power, including negative and fractional exponents (like square roots), with the result shown in full or scientific notation.
Calculate the factorial of any number instantly. Enter n to get the exact value of n! plus the digit count, with the multiplication clearly shown.
Find any Fibonacci number instantly. Enter a term number to get F(n), the running sum, and the full sequence with the classic recurrence explained.
Free fraction calculator to add, subtract, multiply and divide two fractions. Reduces by the GCD and shows the simplified fraction, mixed number and decimal.
Convert any fraction to a decimal instantly. Enter the numerator and denominator to get the decimal value, the percentage, and the division shown.
Find the greatest common divisor (highest common factor) of any numbers instantly. Enter your values to get the GCD, LCM, and the Euclidean steps shown.
Convert hexadecimal to decimal instantly. Enter any hex value with digits 0-9 and A-F to get the base-10 number, binary form, and place-value steps.
Find the least common multiple of two or more numbers instantly. Enter your numbers to get the LCM and GCD with the method clearly explained.
Find the least common multiple (LCM) and greatest common factor (GCF) of two or more whole numbers, with the Euclidean and prime-factorisation methods explained step by step.
Free log calculator that finds the logarithm of any number in any base using the change-of-base rule, and shows the natural log, log base 10 and log base 2.
Solve long division with full steps. Enter a dividend and divisor to get the quotient, remainder, and exact decimal, with each bring-down step shown.
Find the midpoint between two points on a coordinate plane. Free midpoint calculator showing the (x, y) midpoint and segment length with step-by-step working.
Add, subtract, multiply and divide mixed numbers and fractions — with the answer simplified and shown as a fraction, mixed number and decimal. Includes worked examples, a common-denominator method and GCD reducing.
Free modulo calculator that finds the remainder of a divided by b, plus the quotient and the always-positive modulo, for any whole or negative numbers.
Calculate percent error between an experimental and a true value. Free percent error calculator showing the absolute error, signed difference and the full formula.
Calculate a percentage of a number, find what percent one number is of another, or work out the percentage change (increase or decrease) between two values — instantly, with worked examples.
Expand any function f(x) into its Taylor (power) series about a point a. Enter the function, expansion point, and number of terms to see each term and the assembled polynomial.
Free prime number calculator that checks if any whole number is prime or composite using trial division to the square root, and shows the full prime factorization.
Check whether any number is prime instantly. Enter a whole number to see if it is prime or composite, plus its smallest factor and a clear explanation.
Free proportion calculator that solves a/b = c/d for the missing value by cross-multiplication. Enter three numbers, leave one blank, get the answer instantly.
Free Pythagorean theorem calculator. Find the hypotenuse or a missing leg of a right triangle from a2 + b2 = c2, with the formula and worked steps shown.
Free quadratic formula calculator that solves ax²+bx+c=0 for real or complex roots, shows the discriminant, finds the vertex, and explains every step.
Simplify a ratio to its lowest terms and solve a proportion A:B = C:? by cross-multiplication — works for whole numbers and decimals, with an equivalent-ratios table.
Round any number to decimal places, whole numbers, tens, hundreds or thousands. Free rounding calculator showing round half up, round down and round up results.
Reduce any matrix to reduced row echelon form with step-by-step Gauss-Jordan elimination. Free RREF calculator that shows every row operation, the rank and supports fractions.
Free scale factor calculator: divide new size by original size to find the factor, see it as a simplified ratio, and apply it to scale another value instantly.
Free scientific notation calculator that converts any number to scientific, E notation, engineering, and standard decimal form, with the exponent and mantissa shown.
Free slope calculator: enter two points to find the slope of a line, slope-intercept equation y = mx + b, distance and midpoint — with every step shown.
Calculate the volume of a sphere from its radius or diameter. Free sphere volume calculator that also returns surface area with the formula and steps shown.
Find the square root of any number as an exact decimal, and simplify whole-number radicals into the form a√b — with every step shown. Includes a perfect-squares chart and worked examples.
Free triangle area calculator: find the area from base and height (½ × base × height) or from three sides using Heron's formula, with every step shown.
What are math & algebra tools?
Math & algebra tools are free online calculators that solve and explain common numerical problems — percentages, fractions, roots, exponents and logarithms, geometry, sequences, factors and primes. They cover the arithmetic, pre-algebra and basic geometry that appear in homework, finance, construction and data work, and are used by students, teachers and professionals who want a fast, checkable answer.
Math & Algebra tools on Toolzent
Here are the math & algebra calculators currently available, each with worked examples on its page:
| Tool | What it does |
|---|---|
| Percentage Calculator | Finds a percent of a number, what percent one value is of another, and percentage increase or decrease. |
| Mixed Number Calculator | Adds, subtracts, multiplies and divides mixed numbers and improper fractions, and simplifies the result. |
| Square Root Calculator | Computes the square root of a number and shows the simplified radical where one exists. |
| Ratio Calculator | Simplifies ratios, scales them up or down, and solves for a missing term in a proportion. |
| LCM and GCF Calculator | Finds the least common multiple and greatest common factor of two or more whole numbers. |
| Scientific Notation Calculator | Converts numbers between standard form and scientific notation, and computes with very large or small values. |
| Arithmetic Sequence Calculator | Finds the nth term, the common difference and the sum of a sequence with a constant step. |
| Scale Factor Calculator | Works out the scale factor between two sizes and resizes lengths, areas or volumes accordingly. |
| Quadratic Formula Calculator | Solves any quadratic equation, returning both roots and the discriminant with the steps shown. |
| Pythagorean Theorem Calculator | Finds a missing side of a right triangle from the other two using a squared plus b squared equals c squared. |
| Fraction Calculator | Adds, subtracts, multiplies and divides fractions and reduces the answer to lowest terms. |
| Exponent Calculator | Raises a base to a power, including negative and fractional exponents, and shows the expanded value. |
| Logarithm Calculator | Computes a logarithm for any base, plus natural log and log base 10, with the conversion explained. |
| Average Calculator | Returns the mean of a list of numbers along with the sum and count of entries. |
| Circle Calculator | Finds the area, circumference, radius or diameter of a circle from any one known measure. |
| Triangle Area Calculator | Calculates the area of a triangle from base and height or from three known sides. |
| Slope Calculator | Finds the slope and equation of a line from two points, with rise over run shown. |
| Modulo Calculator | Returns the remainder when one number is divided by another, the result of the mod operation. |
| Prime Number Calculator | Tests whether a number is prime and lists its factors to show why it is prime or composite. |
| Proportion Calculator | Solves for a missing value in an equation of two equal ratios using cross-multiplication. |
Common math & algebra formulas
These are the core formulas behind the calculators above, handy to keep nearby when checking your own working.
| Concept | Formula |
|---|---|
| Percent of a number | X% of Y = (X ÷ 100) × Y |
| Percentage change | ((new − old) ÷ old) × 100 |
| Solve a proportion | if a : b = c : x, then x = (b × c) ÷ a |
| Square root | √n is the value r where r × r = n |
| LCM via GCF | LCM(a, b) = (a × b) ÷ GCF(a, b) |
| Quadratic formula | x = (−b ± √(b² − 4ac)) ÷ 2a |
| Pythagorean theorem | a² + b² = c² |
| Circle area | A = π × r² |
| Slope of a line | m = (y₂ − y₁) ÷ (x₂ − x₁) |
| Modulo | a mod n = remainder of a ÷ n |
A quick reminder on terms: a factor divides a number evenly, a prime has exactly two factors, and the discriminant (b squared minus 4ac) tells you how many real roots a quadratic has. Choosing the right operation for a problem is usually harder than the arithmetic itself.
How do I choose the right tool?
Match the tool to the question you are trying to answer:
- Working with percents, discounts or change between two numbers? Use the Percentage Calculator.
- Combining fractions or mixed numbers? Use the Fraction Calculator or the Mixed Number Calculator.
- Need a root, power or logarithm? Use the Square Root Calculator, the Exponent Calculator or the Logarithm Calculator.
- Solving an equation? Use the Quadratic Formula Calculator for quadratics and the Proportion Calculator for a missing ratio term.
- Working on geometry? Use the Pythagorean Theorem Calculator, the Circle Calculator, the Triangle Area Calculator or the Slope Calculator.
- Comparing or scaling quantities? Use the Ratio Calculator or the Scale Factor Calculator.
- Working with whole numbers? Use the LCM and GCF Calculator, the Prime Number Calculator or the Modulo Calculator.
- Summarising a list or a sequence? Use the Average Calculator, the Arithmetic Sequence Calculator, or the Scientific Notation Calculator for very large or small values.
If a fraction needs its lowest terms, the GCF from the LCM and GCF Calculator tells you exactly what to divide by.
Why use Toolzent’s math & algebra tools?
Every calculator is 100% free with no sign-up and nothing to install. The tools run privately in your browser, so your numbers stay on your device and results appear instantly as you type. Each page is mobile-friendly and includes the underlying formula plus worked examples, so you can not only get an answer but understand and verify it — useful whether you are checking homework or a real-world estimate.
For related calculations, explore the Statistics & Probability, Finance & Investing and Unit Converters category hubs.
Frequently asked questions
Are these math & algebra calculators free to use?+
Yes. Every math and algebra tool on Toolzent is 100% free, with no account, no sign-up and no usage limits.
Do the math tools show the steps or just the answer?+
Each tool page returns the result instantly and includes the formula plus worked examples, so you can follow and verify the working.
What is the difference between LCM and GCF?+
The GCF (greatest common factor) is the largest number that divides two values evenly; the LCM (least common multiple) is the smallest number both values divide into.
Which calculator solves a quadratic equation?+
The Quadratic Formula Calculator solves any ax squared plus bx plus c equals 0 using the quadratic formula and reports both roots and the discriminant.
How do I check if a number is prime?+
A prime has exactly two divisors, 1 and itself; the Prime Number Calculator tests a number and lists its factors so you can see why it is prime or composite.
Do I need to install anything or create an account?+
No. The calculators run directly in your browser on desktop or mobile, so there is nothing to install and no account to create.