Row Echelon Form Calculator
Convert a 2x3 or 3x4 augmented matrix to row echelon form using Gaussian elimination with step-by-step operations.
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Percentage, fraction, algebra, and statistics calculators for students and professionals.
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Convert a 2x3 or 3x4 augmented matrix to row echelon form using Gaussian elimination with step-by-step operations.
Convert y = ax² + bx + c to vertex form y = a(x-h)² + k. Find the vertex, axis of symmetry, and direction of the parabola.
Calculate the perimeter of common shapes: rectangle, triangle, circle (circumference), and regular polygon. Also shows the area as a bonus.
Decompose a rational expression into partial fractions. Handles distinct linear factors for degree-2 denominators of the form (x - a)(x - b).
Solve triangles using the law of sines. Find unknown sides and angles from one side, its opposite angle, and another angle.
Calculate the distance between two points in 2D or 3D space using the Euclidean distance formula.
Calculate the centroid (center of mass) of a triangle from three vertex coordinates. Shows the average of x and y values.
Calculate the total surface area of a triangular prism with detailed breakdown of lateral area, base area, and each individual face.
Calculate the volume of a triangular pyramid (tetrahedron) from base area and height, or from base triangle dimensions.
Calculate the total and lateral surface area of a rectangular prism (box) from length, width, and height.
Simplify a three-part ratio to its lowest terms, find percentages, and scale to any total.
Calculate the volume, surface area, and space diagonal of a rectangular prism (box) from its length, width, and height.
Calculate the area, perimeter, diagonals, angles, and side length of a rhombus from the inputs you have.
Check if a number is prime and find its prime factorization. Also shows the nearest primes and divisor count.
Calculate sec, csc, and cot for any angle. Supports degrees and radians with full reciprocal trig values.
Multiply two binomials using the FOIL method. Shows First, Outer, Inner, Last terms and the simplified result.
Perform bitwise XOR on two numbers. Supports decimal, binary, and hexadecimal input and output.
Calculate sin(θ/2), cos(θ/2), and tan(θ/2) using half-angle identities. Supports degrees and radians.
Calculate the diagonal length of a rectangle from its width and height using the Pythagorean theorem.
Calculate the unit rate from any ratio. Find price per unit, speed per hour, or any rate with denominator of 1.
Find the null space (kernel) of a 2x2 or 3x3 matrix. Determines the set of vectors x where Ax = 0.
Calculate the diagonal of a square from its side length, or find the side length from the diagonal.
Calculate eigenvalues and eigenvectors of a 2x2 or 3x3 matrix. Shows the characteristic polynomial and step-by-step solution.
Decompose a 2x2 or 3x3 matrix into lower (L) and upper (U) triangular matrices using Doolittle's method.
Calculate the RMS (root mean square) value from a set of numbers. Used in statistics, physics, and electrical engineering.
Find the reference angle for any angle in degrees or radians. Shows the quadrant and all coterminal trig values.
Calculate the gradient (slope) between two points on a line. Find rise, run, angle, and percentage gradient.
Convert between decimal and two's complement binary representation for 8-bit, 16-bit, or 32-bit integers.
Mortgage, loan, interest, investment, and salary calculators for personal finance.
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Calculate the opportunity cost of a financial decision by comparing the return you could earn on an alternative investment over time.
Calculate the current ratio to measure a company's ability to pay short-term obligations. A standard liquidity metric with a healthy range of 1.5-3.0.
Estimate how much life insurance coverage you need using the DIME method. Factor in debt, income replacement, mortgage, and education costs.
Reverse-engineer the gross pay needed to achieve a desired net (take-home) pay after taxes and deductions.
Calculate sales tax amount, total price with tax, or determine the pre-tax price from a total.
Calculate net debt by subtracting cash and cash equivalents from total debt. A key metric for evaluating company financial health.
Calculate the P/S ratio to value a stock relative to its revenue. Enter market cap and annual revenue, or use per-share figures for the same result.
Convert your hourly wage to an equivalent annual salary, monthly, biweekly, and weekly income based on your work schedule.
Calculate your Required Minimum Distribution from retirement accounts using IRS Uniform Lifetime Table factors.
Calculate certificate of deposit returns using the compound interest formula. Compare CD terms and rates, and see total interest earned over the deposit period.
Calculate the final price after a discount. See your savings amount, final price, and price per unit after single or stacked discounts.
Calculate enterprise value using the Discounted Cash Flow model. Project future cash flows, estimate terminal value, and find the present value of a business.
Estimate your capital gains tax on investments, real estate, or other assets.
Calculate post-judgment interest on court awards. Enter the judgment amount, interest rate, and dates to find total interest owed.
Calculate Purchasing Power Parity to compare how far your money goes in different countries. Convert costs using PPP exchange rates.
Calculate your Net Promoter Score from survey responses. Enter the number of promoters, passives, and detractors to see your NPS instantly.
Calculate your Mega Millions after-tax payout for lump sum and annuity options. See federal and state tax impact on any jackpot.
Calculate vendor markup percentage and compare wholesale to retail pricing. Find the markup, margin, and profit on products you resell.
Calculate the weighted average interest rate across multiple loans. See your combined blended rate and total monthly payment.
Calculate prorated salary for partial pay periods. Enter your annual salary, start or end date, and pay period to find the adjusted amount.
Compare lottery lump sum vs annuity payments over 30 years. See the after-tax value of each option to make a smarter decision.
Calculate Florida sales tax including the 6% state rate plus county discretionary surtax. Enter your county to get the exact combined rate.
Calculate IRS mileage reimbursement for business, medical, or charity driving. Uses the 2025 rate of $0.70/mile for business.
Calculate how long your savings will last with regular withdrawals, accounting for interest earned on the remaining balance.
Calculate YoY growth rate between two periods. Enter this year's and last year's values to find the percentage change.
Calculate California sales tax with the 7.25% base rate plus district taxes. See the total tax and final price for purchases in any CA location.
Count your bills and coins to get a total dollar amount. Enter the quantity of each denomination and see the grand total instantly.
Estimate your California state income tax with 2025 brackets. See your CA tax owed, effective rate, and marginal bracket by filing status.
BMI, calorie, body fat, and nutrition calculators for health-conscious individuals.
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Calculate cardiac output from heart rate and stroke volume. Also shows cardiac index when body surface area is provided.
Find out if you can dunk a basketball. Enter your height and arm length to calculate your standing reach and the vertical jump you need to throw it down.
Calculate how much water to add to dilute spirits or high-proof alcohol to a target ABV using the standard dilution formula.
Calculate the serum anion gap and albumin-corrected anion gap from sodium, chloride, bicarbonate, and albumin lab values.
Calculate your BMI Prime, the ratio of your BMI to the upper limit of normal BMI (25), for a quick assessment of weight status.
Calculate reconstitution volume and injection dosing for research peptides. Given vial amount, water volume, and desired dose, find the injection volume in units and mL.
Estimate calories burned rowing based on intensity, body weight, and duration. Includes MET-based and watts-based calculations.
Calculate Absolute Neutrophil Count from white blood cell count and neutrophil differential to assess immune function and neutropenia risk.
Calculate Homeostatic Model Assessment for Insulin Resistance (HOMA-IR) from fasting insulin and fasting glucose levels.
Convert between running/walking pace formats: min/km, min/mile, km/h, and mph with race time predictions for common distances.
Calculate the BUN-to-creatinine ratio to help distinguish prerenal azotemia from intrinsic renal causes of kidney injury.
Calculate the De Ritis ratio (AST/ALT) for liver disease differential diagnosis. Helps distinguish between alcoholic and non-alcoholic liver conditions.
Score the Berg Balance Scale (BBS) with all 14 items. Total score from 0 to 56 assesses fall risk in older adults and neurological patients.
Calculate theobromine dose and toxicity risk when your dog eats chocolate. Covers milk, dark, baker's, and white chocolate types.
Calculate a baseball pitcher's ERA from earned runs and innings pitched using the official MLB formula.
Estimate how much beer, wine, and liquor to buy for your wedding reception based on guest count, event duration, and drinking habits.
Calculate ideal bedtime and wake-up times to maximize REM sleep cycles. REM sleep increases in later cycles, typically peaking in the 4th and 5th 90-minute cycles.
Estimate your puppy's adult weight based on current weight, age, and breed size category. Uses growth curve multipliers for small, medium, large, and giant breeds.
Calculate Revised Cardiac Risk Index (Lee Index) to estimate perioperative cardiac risk for patients undergoing non-cardiac surgery.
Calculate turkey roasting time and temperature from weight. Covers unstuffed and stuffed turkeys with rest time included.
Estimate tree value using the trunk formula method based on species, trunk diameter, condition, and location.
Calculate a baseball player's batting average from hits and at-bats. Includes OBP estimate, hit breakdown, and historical context.
Score the Tinetti Balance and Gait Assessment (POMA) to evaluate fall risk in older adults. Scores range from 0-28.
Estimate free and bioavailable testosterone from total testosterone, SHBG, and albumin using the Vermeulen method.
Calculate middle cerebral artery peak systolic velocity (MCA-PSV) multiples of the median (MoM) for fetal anemia screening by gestational age.
Estimate when embryo implantation is most likely to occur based on your ovulation date or last menstrual period.
Calculate sourdough bread ingredient amounts from flour weight, hydration percentage, starter percentage, and salt percentage.
Calculate the expected farrowing date from a sow's breeding date. Average swine gestation is 114 days (3 months, 3 weeks, 3 days).
Mechanics, energy, electricity, and motion calculators for physics students.
Convert between rad/s, RPM, and deg/s. Calculate linear velocity from angular velocity and radius.
Calculate rotational kinetic energy using KE = 1/2 I omega squared. Convert between RPM and rad/s for angular velocity.
Calculate specific gravity from substance density and reference density (water at 4°C).
Calculate solar elevation and azimuth angle from latitude, day of year, and time of day.
Calculate air density from temperature, atmospheric pressure, and relative humidity using the ideal gas law.
Calculate thermal resistance for heat sinks and material layers. Find junction temperature from power dissipation.
Calculate kilovolt-amperes (kVA) from voltage and current for single-phase and three-phase electrical systems. Convert between kVA, kW, and amps.
Calculate coil spring rate from wire diameter, coil diameter, number of active coils, and material shear modulus.
Calculate friction loss in pipes using the Hazen-Williams formula. Enter flow rate, pipe diameter, length, and material for pressure drop in PSI.
Calculate audio crossover component values (capacitor and inductor) for first and second-order speaker crossover networks.
Calculate relative humidity from air temperature and dew point temperature using the Magnus formula.
Calculate approximate magnetic declination from geographic coordinates using a simplified dipole model.
Calculate contact lens power from spectacle prescription using vertex distance correction. Essential for prescriptions over +/-4.00 diopters.
Design passive RC or RL low-pass filters. Calculate cutoff frequency, component values, and attenuation.
Calculate true airspeed (TAS) from indicated airspeed (IAS), pressure altitude, and outside air temperature for aviation flight planning.
Estimate quarter-mile elapsed time and trap speed from vehicle horsepower and weight using the Brock Yates / Roger Huntington formula.
Calculate g-force from velocity change and time, or from circular motion radius and speed.
Calculate wet-bulb temperature from dry-bulb temperature and relative humidity. Assess heat stress risk and human survivability limits.
Calculate half-wave dipole antenna length from frequency. Find total length and each leg for common ham and commercial bands.
Calculate energy in watt-hours from power (watts) and time. Convert to kilowatt-hours and estimate electricity cost.
Calculate V-belt or flat belt length from pulley diameters and center distance.
Calculate kinetic energy in foot-pounds from projectile weight (grains) and velocity (fps). Also shows Joules and momentum.
Calculate sunrise and sunset times from latitude, longitude, and date using solar position equations.
Calculate how much the Earth curves over a given distance and how much of a distant object is hidden below the horizon.
Age, date, time, fuel, cooking, and grade calculators for daily use.
Find your expected high school or college graduation year based on current grade level and school year.
Calculate the true cost of meetings based on attendees, hourly rates, and duration.
Calculate your effective DPI for gaming. Compare mouse sensitivity setups and find your cm/360.
Calculate the fuel cost of a trip based on distance, fuel efficiency, and fuel price.
Calculate revolutions per minute from speed and wheel or gear diameter. Convert between RPM, surface speed, and diameter.
Calculate fuel cost, gallons needed, cost per person, and estimated drive time for a road trip.
Calculate the total watch time of a TV series and how long it takes to binge.
Calculate driving time from distance and average speed. See hours, minutes, and arrival time for your trip.
Calculate your Grade Point Average. Enter letter grades and credit hours for up to 6 courses.
Calculate fabric yardage needed from project dimensions and pattern repeat. Works for upholstery, curtains, garments, and general sewing projects.
Calculate interval, total frames, and playback duration for time-lapse photography. Plan your shoot from real-time duration to final video length.
Calculate the antipodal (diametrically opposite) point on Earth from any coordinates. Find what is on the other side of the world.
Calculate the ideal TV mounting height based on screen size, viewing distance, and seating position.
Calculate fabric yardage needed for quilt blocks, sashing, and borders. Enter quilt size and block dimensions to get a full cutting plan.
Determine your vocal range and voice type from your lowest and highest comfortable notes.
Calculate your kill/death ratio and related gaming statistics. See KDA, kills needed for a target ratio, and performance metrics.
Calculate frequency ratios and intervals between musical notes in semitones. Convert between note names and frequencies.
Convert between chmod numeric (octal) and symbolic permission notation. Set read, write, and execute for owner, group, and others.
Calculate PPI from screen resolution and display size. Compare pixel density across monitors, phones, and tablets.
Calculate musical chord notes and intervals from a root note. See notes for major, minor, 7th, diminished, augmented, and suspended chords.
Calculate turbo sizing from engine displacement and target boost. Find the right compressor for your power goals.
Estimate 0-60 mph time from vehicle horsepower, weight, and drivetrain. Compare stock and modified setups.
Calculate and compare price per pound for different products. Find the best deal when buying meat, produce, or bulk items.
Calculate wheel offset, backspacing, and fitment changes when switching wheel widths. Compare old and new wheel setups for vehicle clearance.
Area, volume, concrete, paint, and tile calculators for builders and DIYers.
Calculate how much concrete you need for a slab. Enter length, width, and depth to get cubic yards and number of bags.
Calculate materials for board and batten siding or wainscoting. Get the number of boards, battens, total linear feet, and coverage area.
Calculate spindle RPM from cutting speed and tool or workpiece diameter. Covers milling, turning, and drilling operations with common material presets.
Calculate the area of rectangular, L-shaped, and U-shaped rooms. Enter your room dimensions to get total area in square feet and square meters plus perimeter.
Calculate volume in cubic feet for boxes, rooms, and cylinders. Get results in cubic feet, cubic yards, cubic meters, and gallons with a quantity multiplier.
Calculate pipe rolling offset travel, run, and true offset for plumbing and pipefitting. Supports 22.5, 45, and 60 degree fittings.
Calculate how much soil or topsoil you need for garden beds, raised planters, and landscaping. Get volume in cubic yards, bags needed, and weight estimates.
Calculate the area of rectangles, circles, and triangles. Select a shape and enter the dimensions.
Calculate required CFM (cubic feet per minute) airflow for HVAC systems based on room size and air changes per hour. Includes recommended duct size.
Calculate how many caulk tubes you need for windows, doors, and trim joints. Enter joint dimensions and total length for an accurate materials estimate.
Calculate how much deck stain to buy based on deck area, coverage rate, and number of coats. Get gallons needed and estimated cost.
Calculate aggregate volume and weight for construction fill, road base, and drainage. Enter area dimensions and depth to get cubic yards and tons.
Calculate how much limestone you need by volume and weight. Enter area and depth for driveways, base layers, and landscaping.
Calculate cable or wire sag based on span length, unit weight, and horizontal tension. Get sag distance, sag ratio, and actual cable length.
Calculate GD&T true position from X and Y deviations. Determine if a feature passes or fails its tolerance zone.
Calculate vapor barrier square footage needed for crawl spaces, basement walls, and concrete floors. Accounts for overlaps and waste.
Calculate material tonnage from volume and density. Convert cubic yards or cubic feet to tons for gravel, sand, soil, and other bulk materials.
Calculate bearing load capacity and L10 life expectancy from dynamic load rating, applied load, and speed. Covers radial ball and roller bearings.
Length, weight, temperature, speed, and data unit converters.
Convert steps to miles, kilometers, and calories burned based on your stride length.
Convert between binary and hexadecimal number systems. Also shows decimal and octal equivalents.
Convert torque between inch-pounds and foot-pounds. Also shows newton-meters for metric reference.
Convert inches to centimeters, millimeters, meters, and feet with exact conversion factors.
Convert cents to dollars and count coins. Enter a total in cents or individual coin counts to get the dollar amount.
Convert between quarts and gallons. Also shows liters, pints, cups, and fluid ounces.
Convert gallons to pounds for water and common liquids. Select your liquid for an accurate weight based on its density.
Convert weeks to months, days, and years. Uses the average month length of 4.34524 weeks.
Convert tablespoons to grams for common cooking and baking ingredients. Pick your ingredient for an accurate weight conversion.
Convert pennies to dollars, quarters, dimes, nickels, and coin roll counts.
Convert pixels to inches and inches to pixels at any DPI. Essential for print design, screen layout, and image sizing.
Molarity, dilution, and pH calculators for chemistry students and lab workers.
Convert between concentration units: molarity, mass percent, ppm, ppb, and mg/L. Uses molecular weight and solution density for accurate conversions.
Determine the empirical formula of an organic compound from combustion analysis data (CO₂ and H₂O produced).
Probability, combination, permutation, and z-score calculators for data analysis.
Calculate the Mean Absolute Deviation (MAD) from up to 10 data values. Shows the average distance from the mean.
Find the mode (most frequent value) of a dataset, determine if it is unimodal, bimodal, or multimodal, and see the frequency of each value.
Calculate the range, mid-range, and coefficient of range from your dataset to measure the spread between the minimum and maximum values.
Calculate the relative standard deviation (%RSD) from a data set. RSD equals (standard deviation / mean) × 100.
Calculate a 95% confidence interval for a population mean from sample data. Uses z-score (1.96) for large samples or t-score for small samples.
Find the z-score or x-value for a given cumulative probability. Calculates the inverse CDF (quantile function) of the normal distribution.
Calculate the required sample size for a t-test given effect size, significance level (alpha), and desired statistical power.
Calculate geometric distribution probabilities. Find the probability of first success on trial k, cumulative probabilities, and expected value.
Fit a quartic polynomial (y = ax⁴ + bx³ + cx² + dx + e) to data points using least squares regression.
Fit a quadratic curve (y = ax² + bx + c) to data points using the least squares method. Get R-squared and predictions.
Calculate Simpson's diversity index (D), Simpson's index of diversity (1-D), and Simpson's reciprocal index (1/D) from species counts.
Calculate Cohen's d effect size from two group means and standard deviations. Includes pooled SD, Hedges' g correction, and effect size interpretation.
Sort a list of numbers from smallest to largest. Also shows the range, minimum, maximum, and count.
Calculate sample variance and population variance from a comma-separated data set. Also shows standard deviation and mean.
Convert betting odds (American, decimal, fractional) to implied probability. Compare the true probability to find value bets.
Perform the Mann-Whitney U test for comparing two independent samples. A nonparametric alternative to the two-sample t-test.
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