Financial calculator category
Algebra & Arithmetic calculators
Algebra & Arithmetic calculators: Solve equations, simplify fractions and ratios, and work with exponents, roots and logs. The category holds 22 tools, including the Quadratic Formula Calculator, the Fraction Simplifier Calculator and the Exponent Calculator.
Use Quadratic Formula or Completing the Square for second-degree equations, and Exponent, Root and Logarithm for powers. The Fraction, Fraction Simplifier, Mixed Number to Improper Fraction and Decimal to Fraction calculators handle fractions in each direction. Ratio Simplifier and Proportion solve ratio problems, and Weighted Average and Percent Difference cover comparisons. Sequences have Arithmetic and Geometric calculators, and matrix and vector work uses the Determinant and Dot Product tools. Show your steps.
Among the tools here are Quadratic Formula Calculator, Fraction Simplifier Calculator, Exponent Calculator, Root Calculator, Logarithm Calculator, Ratio Simplifier Calculator, Rounding Calculator, Weighted Average Calculator, and 14 more that follow the same pattern of formula, worked example, limits and sources.
Pick one below. Open it.
Quadratic Formula Calculator
Solve ax² + bx + c = 0 for both roots.
Open calculator →02Fraction Simplifier Calculator
Reduce a fraction to lowest terms using the greatest common factor.
Open calculator →03Exponent Calculator
Calculate base raised to an exponent, including negative and fractional exponents.
Open calculator →04Root Calculator
Calculate the nth root of any value, including cube and higher roots.
Open calculator →05Logarithm Calculator
Calculate the logarithm of a value in any base.
Open calculator →06Ratio Simplifier Calculator
Reduce a ratio to its lowest whole-number terms.
Open calculator →07Rounding Calculator
Round a value to a chosen number of decimal places.
Open calculator →08Weighted Average Calculator
Calculate an average where each value counts by a different weight.
Open calculator →092x2 Matrix Determinant Calculator
Calculate the determinant and trace of a 2x2 matrix.
Open calculator →103x3 Matrix Determinant Calculator
Calculate the determinant and trace of a 3x3 matrix using cofactor expansion.
Open calculator →11Scientific Calculator
A full scientific keypad for trig, log, exponent, root, factorial and memory calculations.
Open calculator →12Fraction Calculator
Add, subtract, multiply or divide two fractions and get the answer in lowest terms plus its decimal value.
Open calculator →13Decimal to Fraction Calculator
Turn a decimal into the closest fraction under a denominator limit you choose.
Open calculator →14Arithmetic Sequence Calculator
Find the last term and the sum of an arithmetic sequence from its first term, common difference and length.
Open calculator →15Geometric Sequence Calculator
Find the last term and the sum of a geometric sequence from its first term, common ratio and length.
Open calculator →16Percent Difference Calculator
Calculate the percent difference between two values, measured against their average.
Open calculator →17Proportion Calculator
Solve a proportion a ÷ b = c ÷ x for the unknown value.
Open calculator →18Roman Numeral Calculator
Convert a whole number from 1 to 3,999 into a Roman numeral.
Open calculator →19Completing the Square Calculator
Rewrite a quadratic in vertex form and find the vertex from its three coefficients.
Open calculator →20Dot Product Calculator
Calculate the dot product, the angle and the cross product magnitude of two 3D vectors.
Open calculator →21Mixed Number to Improper Fraction Calculator
Convert a mixed number into an improper fraction and a decimal.
Open calculator →22Exponential Growth Calculator
Calculate the ending value, the doubling time and the total growth for a steady percentage change per period.
Open calculator →Go deeper
Algebra & Arithmetic guides
Every tool, one table
Algebra & Arithmetic calculators at a glance
Each row shows the headline figure that calculator returns at its own worked-example inputs.
| Calculator | What it answers | Headline output | Worked example |
|---|---|---|---|
| Quadratic Formula Calculator | No real roots means the parabola never crosses the x-axis. | Root 1 (x₁) | 2 |
| Fraction Simplifier Calculator | Use the simplified form for reporting; both fractions are equal. | Simplified numerator | 2 |
| Exponent Calculator | A fractional exponent is a root, so 8^(1/3) is 2, and a negative exponent is a reciprocal, so 2^-3 is 1/8. | Result | 1,024 |
| Root Calculator | Squaring or cubing the result should return close to the original value. | Result | 3 |
| Logarithm Calculator | A logarithm answers: what power gives this base this value? | Logarithm | 2 |
| Ratio Simplifier Calculator | A simplified ratio describes the same proportion with smaller numbers. | Simplified first value | 2 |
| Rounding Calculator | Rounding trades precision for readability; keep full precision for further math. | Rounded value | 3.1 |
| Weighted Average Calculator | Weights should sum to 1 (or 100%) for the result to read as a true average. | Weighted average | 89 |
| 2x2 Matrix Determinant Calculator | A zero determinant means the matrix has no inverse. | Determinant | -2 |
| 3x3 Matrix Determinant Calculator | A zero determinant means the matrix has no inverse. | Determinant | -306 |
| Scientific Calculator | Switch between degree and radian mode before reading a trig result; mixing the two silently changes every answer. | x to the power of y | 1,024 |
| Fraction Calculator | Check homework or a recipe scaling by seeing the reduced fraction and the decimal side by side. | Simplified numerator | 19 |
| Decimal to Fraction Calculator | Pick the denominator limit that matches the tool in your hand: 16 for a ruler, 64 for a drill index, 100 for cents. | Numerator | 11 |
| Arithmetic Sequence Calculator | Total a series that steps by a fixed amount, such as a savings ladder or a seating plan by row. | Last term (aₙ) | 39 |
| Geometric Sequence Calculator | Total a series that grows or shrinks by a fixed multiple, such as doubling or a bouncing ball. | Last term (aₙ) | 4,374 |
| Percent Difference Calculator | Compare two numbers when neither is the starting point. | Percent difference | 22.2% |
| Proportion Calculator | Scale a measurement, a map distance or a mixing ratio by cross-multiplying. | Unknown value (x) | 20 |
| Roman Numeral Calculator | Write a year, a chapter number or a clock face number in Roman numerals: 2026 is MMXXVI, and 4 is IV. | Roman numeral | MMXXVI |
| Completing the Square Calculator | Find the highest or lowest point of a parabola without graphing it. | Vertex x (h) | -3 |
| Dot Product Calculator | Find the angle between two directions or test whether two vectors are perpendicular. | Dot product | 32 |
| Mixed Number to Improper Fraction Calculator | Turn 3 2/5 into 17/5 before you add, subtract or multiply fractions. | Improper numerator | 17 |
| Exponential Growth Calculator | Project a quantity that grows or shrinks by a fixed percent each period. | Ending value | 2,158.9 |
Where people go wrong with algebra & arithmetic numbers
Common slips include losing a negative sign in the quadratic formula, forgetting that a square root has two solutions, and mixing up percent difference with percent change, which use different denominators. Rounding too early compounds errors across steps. A weighted average is not the same as a plain average when the groups differ in size. Always check the answer by substituting it back into the original problem. Check by substituting. It takes seconds.
Background reading
Algebra & Arithmetic guides
- Fractions, decimals and percentages explainedMove between the three ways of writing a part of a whole, add and simplify fractions, and choose the right percent measure for a change or a difference.
Definitions
Algebra & Arithmetic terms
- Determinant : glossary term
- A single number computed from a square matrix that determines whether it can be inverted. A zero determinant means the matrix has no inverse.
- Discriminant : glossary term
- The b²−4ac term inside the quadratic formula, calculated before taking the square root. Its sign alone tells you what kind of solution to expect. Positive means two distinct real roots. Zero means one repeated real root. Negative means no real roots at all, only a complex pair, and those fall outside what a real-number calculator can display.
- Factorial : glossary term
- The product of a whole number and every positive whole number below it, written n!. Used to count arrangements and combinations; 0! is defined as 1.
- Radian : glossary term
- A unit of angle based on the radius of a circle: one full turn equals 2π radians. Trigonometric functions in most programming languages expect radians, not degrees.
Keep exploring
Related calculator categories
Next to the algebra & arithmetic tools, these categories answer the questions that usually come up alongside them.
Common algebra & arithmetic questions
Why does a quadratic equation sometimes have no real solution?
When the discriminant (b²−4ac) is negative, the parabola described by the equation never crosses the x-axis. So there is no real value of x that makes it zero. The equation still has two solutions. But they are complex numbers: outside what a real-number calculator displays.
What's the difference between a root and an exponent?
An exponent raises a value to a power (2³ = 8). A root reverses that operation, asking what value raised to a power gives the result (the cube root of 8 is 2). A root is the same as raising to a fractional exponent: the cube root of x equals x^(1/3).
Why simplify a fraction instead of leaving it as-is?
A simplified fraction represents the exact same value with smaller, easier-to-compare numbers. 6/8 and 3/4 are mathematically identical. The simplified form is just easier to read, compare and combine with other fractions.
Is rounding the same as truncating?
No. Rounding looks at the digit after the cutoff and rounds up or down to the nearest value. Truncating simply cuts off everything after the cutoff regardless of its value. Truncating 2.99 to one decimal gives 2.9. Rounding gives 3.0.
When should I use a weighted average instead of a plain average?
When the values don't all count equally: exam scores worth different percentages of a grade, or portfolio returns weighted by how much is invested in each asset. A plain average silently treats every value as equally important, which is often not true.
Why can't you divide by zero?
Division asks how many times the divisor fits into a number. Zero times any number never gives a non-zero result, so no answer works. The calculators show a dash instead of inventing one.
What is the difference between a common ratio and a common difference?
A sequence with a common difference adds the same amount each step and grows in a straight line. A sequence with a common ratio multiplies by the same amount each step and grows or shrinks faster and faster.
How do I turn a repeating decimal into a fraction?
Set the decimal equal to x, multiply by a power of ten that shifts the repeating block, subtract, and solve. A repeating 0.333 becomes 1/3. The decimal to fraction calculator finds the same answer from a rounded decimal.
What is a mixed number?
A whole number written next to a fraction, such as 3 and 2/5. It equals the improper fraction 17/5. Mixed numbers read naturally, and improper fractions are easier to calculate with.
Why does vertex form help with a quadratic?
It puts the turning point in plain sight. In a(x - h)^2 + k, the vertex is (h, k), so the maximum or minimum of the parabola can be read off without graphing it.
What does it mean for two vectors to be perpendicular?
Their dot product is zero, and the angle between them is 90 degrees. It is the test for a right angle when you have coordinates and not a drawing.
How do Roman numerals show 4 and 9?
By subtraction: a smaller symbol before a larger one is taken away. IV is 4, IX is 9, XL is 40 and XC is 90. The same pattern gives CD for 400 and CM for 900.
People also ask
Algebra & Arithmetic calculator questions
How do I solve a quadratic equation?
Use the quadratic formula, x equals negative b plus or minus the square root of b squared minus 4ac, all over 2a.
What is the difference between percent difference and percent change?
Percent change compares a new value with an original, while percent difference compares two values using their average as the base.
How do I simplify a fraction?
Divide the numerator and denominator by their greatest common factor, which leaves an equal fraction in lowest terms.