UD5 Toolkit
Standard Deviation Calculator – Population & Sample
Compute standard deviation and variance for a dataset, automatically distinguishing between population and sample. See mean, sum of squares, and histogram.
Mathematics Calculators & Solvers
36+ toolsPermutation & Combination Calculator – nPr & nCr
Calculate permutations and combinations easily. Input n and r to see the number of ordered arrangements or unordered selections, with formula and steps.
Factorial Calculator – n! for Integers & Large Numbers
Compute the factorial of any positive integer up to 170+ with full precision output. Also shows double factorial and explains the multiplication steps.
Line Equation Finder – Two Points & Slope-Intercept Form
Generate the equation of a line from two points or a point and slope. Outputs in slope-intercept, point-slope, and standard form with graph coordinates.
Midpoint Calculator – Find the Center Between Two Points
Find the exact midpoint between two points in a 2D plane. Input (x₁, y₁) and (x₂, y₂) to get the midpoint coordinates and a visual representation.
Trigonometry Calculator – Sin, Cos, Tan & Inverse Functions
Compute sine, cosine, tangent, and their inverses. Input degrees or radians to instantly get exact values or decimal approximations for any angle.
Sphere Volume & Surface Area Calculator – V = 4/3πr³
Compute the volume and surface area of a sphere from its radius or diameter. Instant results with units for math assignments and real-world ball sizing.
Triangle Area Calculator – Base, Height & Heron's Formula
Find the area of a triangle using base & height, three sides (Heron's formula), or two sides and included angle. Includes all formulas and unit conversions.
Ratio Simplifier – Reduce Ratios to Lowest Terms
Simplify any ratio (e.g., 15:10) to its lowest terms. Also converts ratios to fractions and percentages, useful for mixing solutions, scaling recipes, or math class.
Variance Calculator – σ² and s² Online for Dataset
Calculate the population and sample variance of a set of numbers. Shows the squared deviations and helps understand data dispersion quickly.
GCD & LCM Calculator – Greatest Common Divisor & Least Common Multiple
Find the greatest common divisor and least common multiple of two or more numbers. Uses prime factorization and Euclidean algorithm with step-by-step output.
Fibonacci Sequence Generator – First N Terms & Golden Ratio
Generate the Fibonacci sequence up to any number of terms. Displays each term, ratios approaching φ, and a visual of the golden spiral for math enthusiasts.
Ellipse Area Calculator – π × a × b Formula
Find the area of an ellipse (oval) from its semi-major and semi-minor axes. Includes circumference approximation for a complete geometric analysis.
Trapezoid Area Calculator – Bases, Height & Median Formula
Calculate the area of a trapezoid using parallel sides and height. Also finds the median length. Useful for land area estimation and geometry homework.
Cylinder Volume Calculator – Tank, Pipe & Can Capacity
Calculate the volume and surface area of a cylinder. Perfect for determining tank capacity, pipe volume, or can dimensions in gallons, liters, or cubic units.
Decimal to Mixed Number Converter – Simple Fraction Form
Turn a decimal number into a mixed number or improper fraction. Shows step-by-step simplification to help understand the conversion process better.
Quadratic Equation Solver – ax² + bx + c = 0 Roots
Solve any quadratic equation by entering coefficients a, b, and c. Computes real and complex roots using the quadratic formula and shows the discriminant.
Percent Change Calculator – Quick Increase & Decrease
Calculate the percentage increase or decrease between two values. Ideal for analyzing stock price changes, revenue growth, or price differences in an intuitive online tool.
Prime Number Racer – Tap the Primes as Fast as Possible
Tap only the prime numbers as they scroll across the screen. Avoid composites and stay alive in this fast‑paced math game that tests your number sense.
Cubic Equation Solver – ax³ + bx² + cx + d = 0
Find all real and complex roots of a cubic polynomial. An online tool for algebra students and engineers that implements Cardano's method and numerical approximation.
Percentage to Fraction Converter – Simplify Math Instantly
Convert any percentage to a simplified fraction and decimal. Great for students learning math, teachers preparing materials, or anyone who needs a quick conversion.
Multiplication Flashcard Practice – Timed Math Drills
Practice times tables with interactive flashcards and a countdown timer. Choose specific numbers to drill, track your score, and improve mental math speed.
Analog Clock Reading Practice – Tell Time to the Minute
Generate random analog clock faces and type the correct time. Adjust difficulty from hours only to 5‑minute intervals to full minute precision.
Slope Calculator – Rise Over Run & Two Points Formula
Calculate the slope of a line from two points or rise and run. Also shows the slope percentage, angle in degrees, and line equation for algebra and construction.
Rounding Mountain – Visual Number Line for Rounding
Type a number and see it on a number line with a “mountain” peak. Visualizes whether it should round up or down to the nearest 10, 100, or 1000.
Coin Flip Streak Tracker – Visualize Randomness
Flip a virtual coin repeatedly and see the longest streak of heads or tails. Visualize how randomness can produce seemingly non‑random patterns.
Math Facts Race – Addition, Subtraction, Multiplication, Division
Answer as many mental math problems as you can in 60 seconds. Choose operation, difficulty, and track your best score over time.
Interactive Geoboard – Stretch Rubber Bands on Pegs
A virtual geoboard where you can stretch virtual rubber bands around pegs to create polygons. Explore perimeter, area, and angles.
Number Base Explainer - Online Learn Binary, Hex
Enter a decimal number and see detailed step‑by‑step conversion to binary, octal, and hex. For students.
Random Number Distribution Visualizer - Online Histogram
Generate random numbers and watch the live histogram. Compare uniform, normal, and exponential distributions.
Conic Sections Playground - Online Circle Ellipse Parabola
Adjust parameters and see how the slice of a cone creates different conic sections. Interactive learning.
Mersenne Prime Checker - Online 2^p‑1 Validation
Check if a number of the form 2^p‑1 is a Mersenne prime. Quick Lucas‑Lehmer test simulation for small p.
Collatz Conjecture Visualizer - Online Hailstone Numbers
Enter a number and see its Collatz sequence graphed. Watch the steps until it reaches 1. Mesmerizing math.
Even or Odd Binary Checker - Online Least Significant Bit
See how a computer decides even/odd by looking at the least significant bit. Enter decimal or binary.
2D Vector Field Plotter - Online Math and Physics
Enter a mathematical function for dx and dy and see the vector field arrows. Perfect for studying differential equations.
Next Prime Number Finder - Online Integer Sequence
Enter any integer and quickly find the next prime number after it. Perfect for hashing and puzzles.