Free Online Calculators

Explore business scenarios, geometry, statistics and engineering formulas with worked examples in free online calculators.

Choose the right tool

Choose the formula that matches the question: a percentage of a value, a percentage change, and percentage-point differences are distinct operations. Enter consistent units and review the worked example before interpreting an estimate.

Available tools

• Percentage Calculator

  Calculate a percentage of a value.

• Percentage Change Calculator

  Calculate the percentage change from an old value to a new value.

• Discount Calculator

  Calculate savings and final price after a percentage discount.

• VAT Calculator

  Add or remove VAT using a rate you supply.

• Loan Payment Calculator

  Estimate fixed monthly payments for an amortizing loan, excluding fees.

• Compound Interest Calculator

  Project compound growth with optional end-of-month contributions.

• Profit Margin & Markup Calculator

  Calculate profit, margin and markup from cost and selling price.

• Tip & Bill Split Calculator

  Calculate a tip and split the total equally.

• Number List Statistics

  Calculate count, sum, mean, median, modes and population standard deviation.

• Weighted Average Calculator

  Calculate a weighted mean from value,weight pairs without headers.

• Ratio Simplifier

  Reduce a two-integer ratio using an exact greatest common divisor.

• Fraction Calculator

  Add, subtract, multiply or divide two exact integer fractions.

• Quadratic Equation Solver

  Solve ax² + bx + c = 0 and report real or complex roots.

• Two Linear Equations Solver

  Solve ax + by = c and dx + ey = f using a 2×2 determinant.

• Power and Logarithm Calculator

  Calculate a power, root or logarithm with an explicit exponent or base.

• Loan Amortization Schedule

  Generate a monthly fixed-rate loan schedule with interest, principal and balance.

• Savings Goal Calculator

  Estimate the monthly contribution needed to reach a savings target.

• Break-Even Calculator

  Calculate units and revenue needed to cover fixed and per-unit costs.

• CAGR Calculator

  Calculate compound annual growth between positive starting and ending values.

• Return on Investment Calculator

  Calculate profit and simple ROI from total returned value.

• Fuel Cost Calculator

  Estimate trip fuel use and cost from distance, liters per 100 km and price per liter.

• Electricity Cost Calculator

  Estimate energy use and cost for a constant-power device.

• Typing Speed Calculator

  Calculate standard five-character words per minute and accuracy.

• Reading Time Estimator

  Estimate reading duration from a supplied words-per-minute rate.

• Triangle Area Calculator

  Area = base × perpendicular height ÷ 2.

• Heron Triangle Calculator

  Area = √[s(s−a)(s−b)(s−c)], with s = perimeter ÷ 2.

• Right Triangle Calculator

  Hypotenuse = √(a²+b²); acute angle = atan2(b,a).

• Circle Calculator

  Area = πr²; circumference = 2πr.

• Ellipse Calculator

  Area = πab; perimeter uses Ramanujan’s second approximation.

• Trapezoid Area Calculator

  Area = (a+b) × height ÷ 2.

• Parallelogram Calculator

  Area = base × height; perimeter = 2(base+side).

• Rhombus Diagonal Calculator

  Area = d₁d₂ ÷ 2; side = √(d₁²+d₂²) ÷ 2.

• Regular Polygon Calculator

  Area = ns² ÷ [4 tan(π/n)].

• Circle Sector Calculator

  Sector area = πr²θ/360; arc length = 2πrθ/360.

• Annulus Area Calculator

  Ring area = π(R²−r²).

• Circular Segment Height Calculator

  Sagitta = r − √(r²−(chord/2)²).

• Sphere Calculator

  Volume = 4πr³/3; surface area = 4πr².

• Cylinder Calculator

  Volume = πr²h; total surface area = 2πr(r+h).

• Cone Calculator

  Volume = πr²h/3; slant height = √(r²+h²).

• Rectangular Prism Calculator

  Volume = lwh; surface area = 2(lw+lh+wh).

• Pyramid Volume Calculator

  Volume = base area × perpendicular height ÷ 3.

• Conical Frustum Calculator

  Volume = πh(R²+Rr+r²)/3.

• Torus Calculator

  Volume = 2π²Rr²; surface area = 4π²Rr.

• Capsule Volume Calculator

  Volume = πr²L + 4πr³/3.

• 2D Distance Calculator

  Distance = √[(x₂−x₁)²+(y₂−y₁)²].

• 3D Distance Calculator

  Distance is the Euclidean length of the coordinate difference.

• Midpoint Calculator

  Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2).

• Line Slope Calculator

  Slope = (y₂−y₁)/(x₂−x₁); intercept = y₁−mx₁.

• Linear Interpolation Calculator

  y = y₁ + (x−x₁)(y₂−y₁)/(x₂−x₁).

• Cartesian to Polar Calculator

  Radius = √(x²+y²); angle = atan2(y,x) in degrees.

• Polar to Cartesian Calculator

  x = r cos θ; y = r sin θ.

• 2D Vector Product Calculator

  Dot product = ax·bx+ay·by; signed cross product = ax·by−ay·bx.

• 3D Cross Product Calculator

  Cross product follows the right-hand rule.

• Normalize 3D Vector

  Divide each component by the vector’s Euclidean magnitude.

• Greatest Common Divisor Calculator

  Euclid’s algorithm returns the greatest common divisor.

• Least Common Multiple Calculator

  LCM = |a × b| / GCD(a,b), with zero handled explicitly.

• Prime Number Checker

  Test divisibility up to the square root of the integer.

• Prime Factorization Calculator

  Divide by successive factors to produce prime powers.

• Integer Divisor Finder

  Find positive divisor pairs up to √n.

• Factorial Calculator

  n! is the exact product of the integers from 1 to n.

• Combinations Calculator

  n choose k = n! / [k!(n−k)!], computed as an exact integer.

• Permutations Calculator

  Ordered selections = n!/(n−k)! without replacement.

• Fibonacci Number Calculator

  F₀ = 0, F₁ = 1; Fₙ = Fₙ₋₁ + Fₙ₋₂.

• Triangular Number Calculator

  Tₙ = n(n+1)/2.

• Arithmetic Sequence Calculator

  Last term = a+(n−1)d; sum = n(first+last)/2.

• Geometric Sequence Calculator

  Term k = a × r^(k−1); add the generated terms.

• Euclidean Modulo Calculator

  Result = ((a % m)+m) % m, constrained to [0,m).

• Modular Exponentiation Calculator

  Repeated squaring computes (base^exponent) mod modulus exactly.

• Perfect Square Checker

  An integer is a perfect square when its integer square root squares back to it.

• Digit Sum and Digital Root

  Repeatedly sum decimal digits until one digit remains.

• Significant Figure Rounding

  Round a finite decimal number to a chosen number of significant figures.

• Nth Root Calculator

  Odd roots accept negative radicands; even real roots require non-negative input.

• Logarithm Base Calculator

  log_b(x) = ln(x)/ln(b).

• Absolute and Relative Error

  Absolute error = |measured−reference|; relative error divides by |reference|.

• Z Score Calculator

  z = (value−mean)/standard deviation.

• Coefficient of Variation Calculator

  CV = standard deviation / |mean| × 100%.

• Standard Error Calculator

  SE of a sample mean = sample standard deviation / √n.

• Mean Confidence Interval Calculator

  Interval = mean ± multiplier × standard error.

• Binomial Probability Calculator

  P(X=k) = C(n,k)p^k(1−p)^(n−k).

• Poisson Probability Calculator

  P(X=k) = e^(−λ)λ^k/k!.

• Bayes Probability Calculator

  P(A|B) = P(B|A)P(A) / [P(B|A)P(A)+P(B|not A)P(not A)].

• Independent Event Probability

  Independent events: both = ab; either = a+b−ab; neither = (1−a)(1−b).

• At Least One Success Probability

  P(at least one) = 1−(1−p)^n.

• Odds and Probability Converter

  Probability = favorable/(favorable+unfavorable).

• Two-Outcome Expected Value

  Expected payoff = p × first + (1−p) × second.

• Simple Interest Calculator

  Interest = principal × annual rate × years.

• Rule of 72 Calculator

  Approximate doubling years = 72/rate; exact annual-compounding years = ln(2)/ln(1+r).

• Purchasing Power Calculator

  Future equivalent cost = current amount × (1+r)^years.

• Unit Price Comparison

  Unit price = price divided by quantity in the same units.

• Hourly Project Rate Calculator

  Effective hourly rate = (fee−expenses)/hours.

• Sales Commission Calculator

  Commission = sales × rate/100; total adds the fixed payment.

• Inventory Turnover Calculator

  Turnover = cost of goods sold / average inventory; days per turnover = period days / turnover.

• Inventory Reorder Point Calculator

  Reorder point = daily demand × lead time + safety stock.

• Economic Order Quantity Calculator

  EOQ = √(2 × annual demand × order cost / annual holding cost per unit).

• Capacity Utilization Calculator

  Utilization percent = actual output / capacity × 100.

• Conversion Rate Calculator

  Conversion rate percent = conversions / visits × 100.

• Advertising Metrics Calculator

  CPM = spend/impressions×1000; CPC = spend/clicks; CPA = spend/conversions.

• Customer Retention Calculator

  Retention percent = (ending customers−new customers)/starting customers×100.

• Customer Churn Calculator

  Churn percent = customers lost / starting customers × 100.

• Overall Equipment Effectiveness

  OEE percent = availability × performance × quality / 10,000.

• Takt Time Calculator

  Takt minutes per unit = available production time / customer demand.

• Paint Quantity Calculator

  Litres = area × coats / coverage × (1+waste/100).

• Tile Quantity Calculator

  Tile count = ceil[area / tile area × (1+waste/100)].

• Concrete Volume Estimate

  Cubic metres = length × width × depth/100.

• Wallpaper Roll Estimate

  Approximate rolls = ceil[area × (1+waste/100)/(roll width × roll length)].

• Mulch Volume Calculator

  Volume m³ = bed length × width × depth/100; litres = m³ × 1000.

• Travel Time Calculator

  Total hours = distance/speed + break minutes/60.

• Running Pace Calculator

  Pace minutes/km = time/distance; speed km/h = distance/time×60.

• Aspect Ratio Size Calculator

  New height = new width × original height / original width.

• Image Print Size Calculator

  Print inches = pixels / DPI; centimetres = inches × 2.54.

• Video File Size Estimate

  Approximate decimal megabytes = bitrate × duration seconds / 8.

• Download Time Calculator

  Ideal seconds = file megabytes × 8 / megabits per second.

• Monthly Data Transfer Estimate

  Decimal gigabytes = kilobytes × views × days / 1,000,000.

• Ohm’s Law Calculator

  Current amperes = voltage/resistance; power watts = voltage²/resistance.

• Series Resistance Calculator

  Series resistance equals the sum of resistances.

• Parallel Resistance Calculator

  Parallel resistance = R₁R₂/(R₁+R₂).

• Voltage Divider Calculator

  Unloaded output voltage = Vin × Rlower/(Rupper+Rlower).

• RC Time Constant Calculator

  Time constant seconds = resistance × capacitance in farads.

• Kinetic Energy Calculator

  Kinetic energy joules = ½mv².

• Gravitational Potential Energy

  Potential energy joules = mass × gravity × height.

• Newton’s Second Law Calculator

  Force newtons = mass × acceleration.

• Momentum Calculator

  Linear momentum kilogram-metres/second = mass × velocity.

• Density Calculator

  Density kg/m³ = mass / volume.

• Wave Speed Calculator

  Wave speed metres/second = frequency × wavelength.

• Centripetal Acceleration Calculator

  Centripetal acceleration = speed²/radius.

• Spring Force and Energy Calculator

  Hooke’s-law force = kx; stored energy = ½kx².

• Cash Runway Calculator

  Net burn = outflow−inflow; runway months = cash/net burn.

• Working Capital Calculator

  Working capital = current assets−current liabilities.

• Liquidity Ratio Calculator

  Current ratio = assets/liabilities; quick ratio = (assets−inventory)/liabilities; cash ratio = cash/liabilities.

• Debt-to-Equity Calculator

  Debt-to-equity ratio = total debt / equity.

• Interest Coverage Calculator

  Interest coverage = EBIT / interest expense.

• Debt Service Coverage Calculator

  DSCR = operating income / debt service for the same period.

• Cash Conversion Cycle Calculator

  Cash conversion days = inventory days+receivable days−payable days.

• Simple Payback Period Calculator

  Simple payback years = initial cost / constant annual net inflow.

• Net Present Value Calculator

  NPV = Σ cash flow at period t divided by (1+rate)^t.

• Conventional Cash Flow IRR Calculator

  Find the period rate making NPV zero for a conventional investment cash-flow series.

• Discounted Payback Schedule

  Discount periodic flows, track cumulative value and estimate the payback crossing.

• Annuity Present Value Calculator

  PV = payment × [1−(1+r)^−n]/r; at zero rate use payment×n.

• Perpetuity Present Value Calculator

  Growing perpetuity value = next payment/(discount rate−growth rate).

• Effective Annual Rate Calculator

  EAR = (1+nominal/m)^m−1.

• Asset Depreciation Schedule

  Build straight-line or double-declining depreciation, bounded by salvage value.

• Fixed Coupon Bond Valuation

  Price is the present value of coupon payments and principal at maturity.

• Weighted Average Cost of Capital

  WACC = E/(E+D)×Re + D/(E+D)×Rd×(1−tax).

• CAPM Scenario Calculator

  Model return = risk-free + beta × (market return−risk-free).

• Customer Acquisition Cost Calculator

  CAC = (marketing spend+sales spend)/new customers.

• Customer Lifetime Value Estimate

  Simplified gross-profit LTV = monthly revenue × margin / monthly churn.

• Customer Acquisition Payback

  CAC payback months = acquisition cost/(monthly revenue×gross margin).

• Subscription Revenue Calculator

  Calculate MRR and annualized run rate from explicit subscription tiers.

• Recurring Revenue Quick Ratio

  Recurring revenue quick ratio = (new+expansion)/(churn+contraction).

• Advertising Profit Scenario

  ROAS = revenue/ad spend; contribution after ads = revenue×margin−spend.

• Payment Fee Gross-Up Calculator

  Required gross = (desired net+fixed fee)/(1−percentage fee).

• Subscription Proration Calculator

  Prorated amount = price × active days/period days.

• Inventory Shrinkage Calculator

  Missing units = recorded−counted; loss value = difference×unit cost.

• Economic Production Quantity

  EPQ = √[2DS/(H(1−D/P))].

• Safety Stock Estimate

  Safety stock = z × daily-demand standard deviation × √lead-time.

• Order Fill Rate Calculator

  Unit fill rate = supplied/requested; full-order rate = complete orders/all orders.

• Dimensional Shipping Weight Calculator

  Volumetric kg = LWH/divisor; chargeable weight is the greater of actual and volumetric.

• Freight Cost Allocation Calculator

  Allocate a freight total proportionally to non-negative item weights.

• FIFO Inventory Cost Calculator

  Calculate FIFO cost of goods sold and ending inventory from purchase lots.

• Rectangular Box Packing Estimator

  Compare six axis-aligned box orientations using floor divisions.

• Recipe Portion Scaler

  Scale each ingredient quantity from an original serving count to a target count.

• 3D Print Material Cost Calculator

  Mass = cylindrical filament volume × density; cost = mass kg × price/kg.

• Battery Runtime Estimate

  Estimated hours = Ah×V×usable fraction/load watts.

• Photography Exposure Value Calculator

  EV100 = log₂(f-number²/shutter seconds)−log₂(ISO/100).

• Depth of Field Calculator

  Hyperfocal H = f²/(N c)+f; near/far limits follow the thin-lens model.

• Camera Field of View Calculator

  Field angle = 2 atan(sensor dimension/(2×focal length)).

• Ideal Projectile Motion Calculator

  Same-height flight: time = 2v sinθ/g; range = v² sin(2θ)/g.

• Ideal Free Fall Calculator

  From rest: time = √(2h/g); impact speed = √(2gh).

• Buoyant Force Calculator

  Buoyant force = fluid density × displaced volume × gravity.

• Hydrostatic Pressure Calculator

  Gauge pressure = ρgh; absolute pressure = surface pressure+ρgh.

• Ideal Gas Pressure Calculator

  Pressure = nRT/V, with R = 8.31446261815324 J/(mol K).

• Sensible Heat Calculator

  Heat joules = mass × specific heat × temperature change.

• Linear Thermal Expansion Calculator

  Length change = original length × expansion coefficient × temperature change.

• Ideal Mixing Temperature Calculator

  Equilibrium temperature = (m₁c₁T₁+m₂c₂T₂)/(m₁c₁+m₂c₂).

• Pipe Flow Velocity Calculator

  Velocity = volumetric flow / circular internal cross-sectional area.

• Reynolds Number Calculator

  Reynolds number = density × speed × characteristic length / dynamic viscosity.

• Mach Number Calculator

  Mach number = speed / local sound speed.

• Independent Sound Level Adder

  Combine independent intensity levels: total dB = 10 log₁₀(Σ10^(L/10)).

• Free-Field Sound Distance Estimate

  New level = reference level−20 log₁₀(new distance/reference distance).

• Series RLC Impedance Calculator

  X = 2πfL−1/(2πfC); impedance magnitude = √(R²+X²).

• LC Resonant Frequency Calculator

  Resonant hertz = 1/(2π√LC).

• AC Power Triangle Calculator

  Apparent power = VI; real power = VI×PF; reactive magnitude = VI√(1−PF²).

• Compound Gear Train Calculator

  Output rpm = input rpm × driver1/driven1 × driver2/driven2.

• Open Belt Length Estimate

  Approximate open-belt length = 2C+π(D+d)/2+(D−d)²/(4C).

• Machining Cutting Speed Calculator

  Surface speed metres/min = π × diameter mm × rpm / 1000.

• Lead Screw Linear Feed Calculator

  Linear feed mm/min = lead × rpm.

• Friction Force Calculator

  Limiting/sliding friction magnitude = coefficient × normal force.

• Shaft Twist Estimate

  Twist radians = torque × length / (shear modulus × polar second moment).

• Circular Motion Force Calculator

  Required centripetal force magnitude = mass × (2πrpm/60)² × radius.

• Constant-Deceleration Stopping Estimate

  Distance = speed×reaction time + speed²/(2×deceleration).

• Equivalent Spring Constant Calculator

  Parallel k = k1+k2; series k = k1k2/(k1+k2).

• Numeric Percentile Calculator

  Compute linear-interpolated percentiles and quartiles from a numeric sample.

• Geometric and Harmonic Mean Calculator

  Calculate geometric, harmonic and quadratic means for positive values.

• Median Absolute Deviation Calculator

  Compute median absolute deviation and an explicitly scaled robust spread.

• Trimmed Mean Calculator

  Remove an equal fraction from both sorted tails and summarize the retained values.

• Skewness and Kurtosis Calculator

  Calculate population central-moment skewness and excess kurtosis.

• Equal-Width Histogram Builder

  Count numeric values into a selected number of equal-width bins.

• Empirical Distribution Builder

  Return sorted distinct values and cumulative observed probabilities.

• Exponential Smoothing Calculator

  Smooth a sequence using S₀=x₀ and Sₜ=αxₜ+(1−α)Sₜ₋₁.

• Autocorrelation Calculator

  Compute a mean-centered, full-variance-denominator autocorrelation at one lag.

• Numeric Cross-Correlation Calculator

  Compute full unnormalized discrete cross-correlation of two numeric arrays.

• Discrete Sequence Convolution

  Compute full discrete convolution between two numeric sequences.

• Discrete Fourier Transform Calculator

  Calculate the forward DFT of a bounded real-valued sequence.

• Simple Linear Regression Calculator

  Fit y = intercept+slope×x and report residual sum of squares and R².

• Weighted Linear Regression Calculator

  Fit an intercept and slope to [x,y,positive weight] observations.

• Lagrange Polynomial Interpolator

  Evaluate the unique interpolating polynomial at a supplied x coordinate.

• Sampled Data Integration Calculator

  Integrate ordered [x,y] observations with the trapezoidal rule.

• Sampled Data Derivative Calculator

  Estimate interior derivatives using adjacent secant spans and one-sided endpoints.

• Polynomial Derivative and Integral

  Differentiate and integrate ascending-order coefficients; constant of integration is set to zero.

• Polynomial Arithmetic Calculator

  Add, subtract or multiply polynomials represented by ascending-order coefficient arrays.

• Bracketed Polynomial Root Finder

  Use bisection on a real polynomial whose endpoint values have opposite signs.

• Complex Number Arithmetic

  Compute sum, difference, product and quotient of two complex numbers.

• Trigonometric Value Calculator

  Evaluate sine, cosine and tangent using degree input.

• Continued Fraction Expansion

  Expand one finite real value into a bounded simple continued fraction.

• Normal Distribution Probability

  Calculate an approximate normal CDF and density using supplied mean and spread.

• Exponential Distribution Calculator

  CDF = 1−e^(−λx); density = λe^(−λx); mean = 1/λ.

• Weibull Distribution Calculator

  CDF = 1−exp[−(x/λ)^k]; density = (k/λ)(x/λ)^(k−1)exp[−(x/λ)^k].

• Chi-Square Goodness-of-Fit Statistic

  Compute Σ(observed−expected)²/expected from [observed,expected] count pairs.

• Contingency Table Chi-Square Statistic

  Compute independence expected counts and Pearson chi-square for a count table.

• One-Sample T Statistic Calculator

  Compute t = (sample mean−reference mean)/(sample standard deviation/√n).

• Welch Two-Sample T Statistic

  Calculate Welch’s t statistic and approximate degrees of freedom for independent samples.

• Paired Sample T Statistic

  Apply a one-sample t statistic to second-minus-first paired differences.

• Cohen D Effect Size Calculator

  Calculate the difference in sample means divided by pooled sample standard deviation.

• Binary Classification Metrics

  Calculate accuracy, precision, recall, specificity and F1 from a confusion count table.

• Prediction Error Metrics Calculator

  Compute MAE, MSE, RMSE and R² from [actual,predicted] pairs.

• Wilson Proportion Interval Calculator

  Wilson interval uses center (p+z²/(2n))/(1+z²/n) and its score half-width.