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Free Math Calculators — Algebra, Graphing, Roots & More | Frizbo
Algebra · Geometry · Calculus · Number Theory

Math tools that give you
answers, not headaches

From quadratic equations to scientific notation — every calculator here does one thing well. No signup, no ads, no friction.

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Algebra
Roots & Powers
Trig & Logs
Notation
Graphing
Featured Calculator
Quadratic Formula Calculator
Enter a, b, c from ax² + bx + c = 0. Results include discriminant and both roots.
x² +
x +
= 0
Roots
Enter values above and hit Solve
Also Try
Scientific Calculator
sin, cos, tan, log, ln, e, π, exponents
Graphing Calculator
y = f(x) → intercepts, vertex, intersections
Root Calculators
√x · ∛x · nth root → exact + decimal form
Exponent & Logs Calculator
bⁿ · log₁₀(x) · ln(x) · logₐ(x)
Browse Math Calculators
7 tools
Why these math tools exist

Math is hard enough without fighting your calculator. These tools remove the friction — you type in the numbers, get the answer, and move on. Each one is built for a specific job, not as a general-purpose tool trying to do everything poorly.

For students, the right use is to check your work after attempting the problem. Type in the equation after you've tried it. If you got it wrong, the step-by-step output shows exactly where the calculation diverged. That's how you actually learn from a mistake rather than just copying a correct answer.

The discriminant — what it tells you before you solve

Before solving a quadratic, the discriminant (b² − 4ac) tells you what kind of answers to expect. Positive means two distinct real roots. Zero means one repeated root. Negative means complex numbers — and if you were expecting real answers, that's a sign of a sign error somewhere in your setup.

x = (−b ± √(b² − 4ac)) / 2a

Δ > 0 → two real roots
Δ = 0 → one real root (double)
Δ < 0 → complex roots (a ± bi)

Checking the discriminant first saves you from expecting a clean answer when none exists.

Math Operations Quick Reference
Operation Notation Example Result Calculator to Use
Square root√x = x^(1/2)√14412Root Calculator
Cube root∛x = x^(1/3)∛273Root Calculator
Negative exponentx⁻ⁿ = 1/xⁿ2⁻³0.125Exponent & Logs
Natural logln(x) = logₑ(x)ln(e²)2Exponent & Logs
Common loglog₁₀(x)log(1000)3Scientific Calculator
LCM of two numbersLCM(a,b) = ab / GCF(a,b)LCM(4, 6)12Factorization
GCF of two numbersGCF via prime factorsGCF(24, 36)12Factorization
Scientific notationa × 10ⁿ (1 ≤ a < 10)5,2005.2 × 10³Scientific Notation
Quadratic roots(−b ± √Δ) / 2ax²+5x+6=0x=−2, x=−3Quadratic Calculator
Practical Tips
Getting more out of each tool
Set your angle mode before any trig calculation
Scientific calculators default to degrees. Calculus and most higher math uses radians. Sin(90°) = 1, but sin(90 radians) ≈ 0.894 — a completely different answer. Check your mode before running any trig function.
Rule: degrees for geometry, radians for calculus and physics
Roots are fractional exponents — use that to your advantage
√x = x^(1/2) and ∛x = x^(1/3). When you hit an nth root problem in an expression with other exponents, convert to fractional form so you can apply exponent rules rather than treating roots as a separate operation.
e.g. x^(1/2) × x^(1/3) = x^(5/6) — one step, no confusion
Use LCM to find the right common denominator first time
When adding fractions like 5/12 + 7/18, guessing a common denominator wastes time. The LCM of 12 and 18 is 36 — the smallest number both divide into cleanly. Starting with LCM means you'll never need to simplify the result afterward.
LCM(12, 18) = 36 → 15/36 + 14/36 = 29/36
Multiply scientific notation by adding exponents, not multiplying them
When multiplying (3 × 10⁴) × (2 × 10³), multiply the coefficients (3 × 2 = 6) and add the exponents (4 + 3 = 7), giving 6 × 10⁷. The most common mistake is multiplying the exponents instead — which gives a completely wrong order of magnitude.
(a × 10ⁿ) × (b × 10ᵐ) = (a×b) × 10^(n+m)
FAQ
Frequently asked questions
What does a negative discriminant mean in a quadratic equation? +
It means the equation has no real roots — the solutions are complex numbers (involving i, the square root of −1). If you expected real answers, check your a, b, c values for a sign error.
What's the difference between log and ln? +
log (or log₁₀) uses base 10 — log(1000) = 3 because 10³ = 1000. ln uses base e (≈2.718) — ln(e²) = 2. Natural log appears in calculus, growth models, and physics; common log is more common in chemistry and engineering.
When would I need the nth root instead of a square or cube root? +
Nth roots appear in compound interest (finding average growth rate over n periods), statistics (geometric mean), and higher-level algebra. If you need the 5th root of 32, that's 2 — because 2⁵ = 32.
Is there a sign-up required to use Frizbo's math calculators? +
No account, email, or registration is needed for any calculator on Frizbo. Every tool is free and opens immediately.
Why does my graphing calculator show a different result than my hand calculation? +
Usually an angle mode mismatch (degrees vs radians) or operator precedence — 2+3×4 is 14, not 20. Use parentheses to make the order of operations explicit when entering complex expressions.
How do I convert a decimal to scientific notation correctly? +
Move the decimal point until you have a number between 1 and 10, then count the steps. Moving left means a positive exponent; moving right means negative. 0.0052 → 5.2 × 10⁻³. The scientific notation calculator does this automatically.
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Every calculator on this page is built on standard mathematical formulas and intended to give accurate results. That said, for graded work, always verify against your textbook or professor's method — different conventions (degree vs radian, log base) can produce different correct answers depending on context. Use these tools to check and learn, not to replace understanding.

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