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Complete ToolPatch tools directory
ToolPatch is a growing collection of focused utilities and practical workflow toolkits. Each page handles one task with clear inputs, fast results, and usable outputs.
Toolkits for common workflows
Start with a workflow when the job spans several small tools, assumptions, or handoff steps.
Startup Unit Economics Toolkit
Build, stress-test, and communicate your core economics in one workflow.
Network Troubleshooting Toolkit
Diagnose addressing, DNS, and transport bottlenecks quickly.
Lab and Chemistry Calculations Toolkit
Plan solution preparation, dilution, gas-law, reaction-yield, and pH checks with visible chemistry assumptions.
Project Delivery Planning Toolkit
Forecast schedule and delivery risk using practical PM metrics.
Engineering Field Calcs Toolkit
Fast first-pass engineering calculations for site and workshop decisions.
Chart Generators Toolkit
Choose the right chart generator for radar, spider, radial, Gantt, Sankey, bubble, Pareto, funnel, waterfall, trend, comparison, and distribution views.
Marine Navigation Calculators Toolkit
Use practical marine navigation calculators for CPA/TCPA, under-keel clearance, tide windows, route distance, set and drift, fuel range, ETA, anchoring, COLREGs encounter checks, and vessel turning estimates.
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Science & Math
Featured
Flywheel Energy Calculator
Calculate kinetic energy stored in a rotating flywheel.
Determine the kinetic energy stored in a flywheel based on its moment of inertia and angular velocity, or derived from its shape, mass, radius, and RPM.
Science & Math
Arithmetic Sequence Solver
Find nth term and sum of an arithmetic progression from a, d, and n.
Solve arithmetic progression problems with first term, common difference, and number of terms. Great for school math, exam preparation, and quick sequence verification.
Science & Math
Binomial Probability Calculator
Compute exact and cumulative binomial probabilities for n, k, p.
Great for probability exercises, risk estimation, and stats exam prep.
Science & Math
Blackbody Radiation Calculator
Calculate Wien peak wavelength and Stefan-Boltzmann radiation power.
Estimate blackbody spectral peak and total emitted power from temperature and emitting area.
Science & Math
Boyle's Law Calculator
Calculate gas pressure and volume relationships at constant temperature.
Apply Boyle's Law (P₁V₁ = P₂V₂) to solve for unknown pressure or volume. Enter any 3 values to calculate the 4th.
Science & Math
Charles' Law Calculator
Calculate gas volume and temperature relationships at constant pressure.
Apply Charles' Law (V₁/T₁ = V₂/T₂) to solve for unknown volume or temperature. Automatically converts Celsius to Kelvin.
Science & Math
Circle Calculator
Calculate diameter, circumference, and area from a circle radius.
Input radius and get all key circle measurements with precise decimal outputs. Suitable for geometry practice, engineering checks, and classroom demos.
Science & Math
Cylinder Volume Calculator
Calculate cylinder volume and surface area from radius and height.
Compute volume, total surface area, lateral area, and base area from cylinder dimensions.
Science & Math
Damped Oscillator Calculator
Solve damped spring-mass response and classify damping regime.
Model m*x'' + c*x' + k*x = 0 with initial conditions to compute displacement, damping ratio, and settling behavior.
Science & Math
Density Calculator
Calculate density from mass and volume.
Compute density using the fundamental formula ρ = m/V. Useful for physics, chemistry, and material science applications.
Science & Math
Dilution Calculator
Use C1V1=C2V2 to solve dilution and solution prep problems.
Determine unknown concentration or volume for dilution planning with one equation. Great for lab workflows, stock solution prep, and chemistry practice.
Science & Math
Distance Speed Time Calculator
Solve for distance, speed, or time using the standard motion formula.
Choose whether to solve for distance, speed, or time and provide the remaining values. Useful for travel planning, logistics estimation, and physics homework checks.
Science & Math
Doppler Shift Calculator
Calculate observed frequency shift from source/observer relative motion.
Evaluate Doppler frequency shift for wave systems using source and observer speeds with directional motion.
Science & Math
Euler Method ODE Solver
Approximate ODE solutions with the forward Euler method.
Numerically solve dy/dx = a*x + b*y + c from initial conditions, step size, and step count.
Science & Math
Exponential Growth Decay Calculator
Model growth or decay over periods with compounding behavior.
Calculate exponential growth/decay trajectories using an initial value, periodic rate, and period count.
Science & Math
Factorial Permutation Combination Calculator
Compute n!, nPr, and nCr for combinatorics and probability problems.
Enter n and r to calculate factorial, permutations, and combinations in one place. Useful for exam prep, probability work, and algorithmic problem solving.
Science & Math
Fibonacci Sequence Generator
Generate Fibonacci numbers and inspect nth term and sequence sum.
Choose how many terms to generate and instantly get the sequence, nth value, and total sum. Great for math practice, coding interviews, and algorithm demonstrations.
Science & Math
Force & Area to Pressure Calculator
Calculate pressure from force and area.
Compute pressure using P = F/A. Useful for mechanical engineering, hydraulics, and physics applications.
Science & Math
Fraction Simplifier
Reduce fractions to simplest form and convert to decimal instantly.
Enter numerator and denominator to simplify fractions using GCD and view decimal form. Helpful for math homework, tutoring sessions, and quick arithmetic checks.
Science & Math
Frequency Period Converter
Convert between frequency and period.
Bidirectional converter between frequency (Hz) and period (seconds) using f = 1/T. Useful for electronics, signal processing, and wave analysis.
Science & Math
GCD LCM Calculator
Find greatest common divisor and least common multiple for two integers.
Input two integers to calculate GCD, LCM, and whether they are coprime. Great for number theory basics, classroom exercises, and programming prep.
Science & Math
GPA Calculator
Compute GPA from course credits and grade points.
Enter credits and grade points per course to calculate weighted GPA. Helpful for semester planning, scholarship targets, and academic progress tracking.
Science & Math
Ideal Gas Law Calculator
Solve pressure, volume, moles, or temperature with PV=nRT.
Use the ideal gas law to solve one missing variable given the other three. Great for gas-law homework, exam prep, and quick unit-aware checks.
Science & Math
Kinetic Energy Calculator
Compute kinetic energy and momentum from mass and velocity.
Calculate energy with KE = 1/2 m v² and momentum p = m v in one page. Useful for mechanics problems and practical motion estimates.
Science & Math
Lens Imaging Calculator
Solve thin-lens image distance, magnification, and orientation.
Use the thin lens equation to determine real/virtual image characteristics and image size scaling.
Science & Math
Linear Regression Calculator
Fit a best-fit line from point data and compute r and R².
Enter x,y pairs to estimate slope, intercept, and correlation quality.
Science & Math
Logarithm Calculator
Compute logarithms for custom base and value inputs.
Solve log_b(x) quickly and verify with exponent reconstruction.
Science & Math
Matrix 2x2 Analyzer
Analyze determinant, inverse, trace, and eigenvalues for 2x2 matrices.
Useful for linear algebra classes, engineering math, and matrix sanity checks.
Science & Math
Molarity Calculator
Solve molarity, moles, or volume using M = n/V.
Calculate solution concentration and dilution prep values from moles and volume. Useful for lab prep, chemistry coursework, and quick concentration checks.
Science & Math
Newton Second Law Calculator
Solve force, mass, or acceleration using F = m * a.
Use Newton's second law to solve one unknown variable when the other two are known. Helpful for physics classes, engineering checks, and quick unit-based sanity tests.
Science & Math
Ohms Law Calculator
Solve voltage, current, or resistance and compute electrical power.
Apply Ohm's law (V = I * R) to electrical circuit basics and derive missing values. Includes quick power estimate using P = V * I.
Science & Math
Orbital Mechanics Calculator
Compute circular orbital speed, escape speed, and orbital period.
Estimate orbital dynamics around a central body from mass and altitude with physically grounded equations.
Science & Math
Percentage Change Calculator
Compute absolute and percentage increase/decrease between two values.
Enter initial and final values to calculate both absolute change and percent change instantly. Useful for pricing updates, KPI shifts, trend reports, and quick sanity checks.
Science & Math
pH Calculator
Convert hydrogen ion concentration to pH and classify acidity/basicity.
Compute pH and pOH from [H+] or derive [H+] from pH quickly. Useful for acid-base questions, buffer prep, and classroom exercises.
Science & Math
Polynomial Derivative Evaluator
Evaluate cubic polynomial derivatives and curvature at a chosen x value.
Compute f(x), f'(x), and f''(x) for ax^3+bx^2+cx+d with instant output.
Science & Math
Prime Number Checker
Check whether a number is prime and view factors when it is not.
Enter an integer to test primality and classify the number quickly. Helpful for schoolwork, coding practice, and cryptography fundamentals.
Science & Math
Projectile Motion Calculator
Estimate flight time, max height, and range from launch speed and angle.
Solve projectile motion assuming no air resistance and equal launch/landing heights. Great for introductory mechanics practice and trajectory intuition.
Science & Math
Quadratic Equation Solver
Solve ax² + bx + c = 0 with real or complex roots.
Quickly compute discriminant and roots for quadratic equations with clear output formatting. Suitable for students, tutors, and engineering pre-checks.
Science & Math
Random Number Generator
Generate random numbers with range, count, and uniqueness options.
Create integer or decimal random samples with configurable bounds and uniqueness constraints.
Science & Math
RC Circuit Transient Calculator
Analyze capacitor voltage/current over time for RC charge and discharge.
Compute RC time constant, transient voltage/current response, and milestone times (63%, 90%, 99%).
Science & Math
Reaction Yield Calculator
Calculate percent yield and loss from theoretical and actual yield values.
Enter theoretical and actual yield to evaluate reaction efficiency. Helpful for lab reports, stoichiometry checks, and process optimization basics.
Science & Math
Sphere Volume Calculator
Calculate sphere volume and surface area from radius.
Compute volume, surface area, and diameter from sphere radius using standard geometric formulas.
Science & Math
Standard Deviation Calculator
Calculate mean, variance, and standard deviation for a dataset.
Paste numeric values to compute population and sample statistics quickly. Useful for analytics, classroom assignments, and data quality checks.
Science & Math
Symbolic Equation Solver
Solve linear and quadratic equations in x with symbolic steps.
Solve equations in one variable (`x`) on a single page and get both simplified form and final roots. This tool accepts equations such as `3x + 9 = 0` and `2x^2 - 5x - 3 = 0`, then normalizes terms to standard form, applies the correct method, and displays symbolic steps you can follow or reuse in notes. It is intended for algebra practice, quick verification before coding formulas, and engineering sanity checks. Current scope is polynomial equations up to degree 2 with real coefficients.
Science & Math
Symbolic Integral Calculator
Integrate polynomial expressions symbolically and evaluate definite bounds.
Find antiderivatives for polynomial terms (e.g. 3x^2 - 4x + 7) and optionally compute definite integral values.
Science & Math
Triangle Analyzer
Analyze triangle validity, perimeter, area, angles, and type.
Enter side lengths to classify triangles and compute key geometry outputs for coursework and design.
Science & Math
Vector Operations Calculator
Run dot product, angle, magnitude, sum, difference, and cross product.
Compute core 2D/3D vector operations for mechanics, graphics, and linear algebra tasks.
Science & Math
Wave Speed Calculator
Solve wave speed, frequency, or wavelength using v = f * lambda.
Choose which variable to solve and compute wave relationships for sound, light, or general wave problems. Includes period output from frequency.
Science & Math
Weighted Average Calculator
Compute weighted average from value and weight lists.
Ideal for grading, portfolio weighting, KPI scoring, and multi-factor decision models.
Science & Math
Z-Score Percentile Calculator
Convert values to z-scores and estimate normal-distribution percentile.
Useful for test scores, benchmarking, and statistical interpretation.