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Golden Ratio Calculator
Split any length into two golden sections, or find the matching side from the longer or shorter one. You also get a golden rectangle preview and a φ-based scale of sizes for layouts, typography and woodworking.
I know the…
Width of a page, canvas, layout or any length
Enter your values to see the result.
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How to use the Golden Ratio Calculator
- Choose what you know: the total length, the longer side a or the shorter side b.
- Enter the length and pick a unit.
- Read the golden sections a and b and the whole a + b.
- Use the φ scale table for harmonious font sizes, margins or panel widths.
- Copy the results or download the scale as CSV.
Golden ratio formulas
Two lengths a (longer) and b (shorter) are in the golden ratio when a ÷ b = (a + b) ÷ a = φ. Solving that gives φ = (1 + √5) ÷ 2 ≈ 1.6180339887, with the handy identities φ² = φ + 1 ≈ 2.618034 and 1 ÷ φ = φ − 1 ≈ 0.618034.
| You know | Longer side a | Shorter side b | Whole a + b |
|---|---|---|---|
| Whole length T | T ÷ φ ≈ T × 0.618034 | T ÷ φ² ≈ T × 0.381966 | T |
| Longer side a | a | a ÷ φ ≈ a × 0.618034 | a × φ |
| Shorter side b | b × φ ≈ b × 1.618034 | b | b × φ² ≈ b × 2.618034 |
Common golden splits
| Total | Longer section (61.8%) | Shorter section (38.2%) | Typical use |
|---|---|---|---|
| 960 px | 593.31 px | 366.69 px | Content and sidebar widths |
| 1200 px | 741.64 px | 458.36 px | Wide page layout |
| 1920 px | 1,186.63 px | 733.37 px | Full HD hero split |
| 100 cm | 61.80 cm | 38.20 cm | Furniture and frames |
| 8 ft | 4.94 ft | 3.06 ft | Shelf or panel placement |
For a design scale, multiply a base value by φ for every step up (16 → 25.89 → 41.89 px) and divide by φ for every step down (16 → 9.89 → 6.11 px). Rounding to whole pixels or to nearby Fibonacci numbers (8, 13, 21, 34, 55) keeps the feel of the ratio with practical sizes.
Frequently asked questions
What is the golden ratio?
The golden ratio φ (phi) is about 1.6180339887. Two lengths a > b are in the golden ratio when a ÷ b equals (a + b) ÷ a. Its exact value is (1 + √5) ÷ 2.
How do I divide a length by the golden ratio?
Divide the total by φ to get the longer section: a = total ÷ 1.618034, which is about 61.8% of the total. The shorter section is the rest, b = total − a, about 38.2%. For 1200 px that gives about 741.64 px and 458.36 px.
How do I find the other side of a golden rectangle?
If you know the long side, divide it by 1.618034 to get the short side. If you know the short side, multiply it by 1.618034 to get the long side.
How is the golden ratio used for font sizes?
A golden type scale multiplies a base size by φ for each step up and divides by φ for each step down. From a 16 px body size the next sizes up are about 25.9 px and 41.9 px, and the step down is about 9.9 px.
What is the link between the golden ratio and Fibonacci numbers?
The ratio of consecutive Fibonacci numbers (8/5, 13/8, 21/13, …) gets closer and closer to φ. That is why Fibonacci-based sizes such as 5, 8, 13, 21 are often used as a whole-number approximation of a golden scale.
Why is the golden ratio 61.8% and 38.2%?
1 ÷ φ ≈ 0.618 and 1 ÷ φ² ≈ 0.382, and these two add up to exactly 1. So the longer section is 61.8% of the whole and the shorter section is 38.2%.
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Cost, monthly savings, break-even month and net savings.Closing Cost CalculatorEstimate itemized closing costs, prepaids and total cash to close for a home purchase.Property Tax CalculatorAnnual and monthly property tax from value, assessment ratio, exemptions and % or mill rate.Rent Affordability CalculatorHow much rent you can afford with the 30% rule, the 40x income rule and your debts.Loan Comparison CalculatorCompare up to three loans: monthly payment, total interest, fees, total cost and APR.Balloon Payment CalculatorMonthly payment and lump-sum balloon due on an amortizing or interest-only loan.Business Loan CalculatorBusiness loan payments (monthly, weekly or daily), total cost and effective APR with fees.Interest Rate CalculatorSolve a loan's interest rate (APR) from the amount, payment and term using Newton's method.Loan-to-Value CalculatorLTV, CLTV and HCLTV ratios, home equity, and the pay-down needed to drop PMI.Yield to Maturity CalculatorFind a bond's yield to maturity, current yield and yield to call from its price and coupon.Bond Price CalculatorPrice a bond from its coupon, yield and term, with premium or discount and a cash flow table.Stock Average CalculatorAverage cost of several stock buys, plus how many shares to buy to reach a target average.Position Size CalculatorHow many shares or units to trade so a stop-loss risks only a set share of your account.P/E Ratio CalculatorPrice-to-earnings ratio, earnings yield and PEG ratio from share price, EPS and growth.EPS CalculatorBasic and diluted earnings per share from net income, preferred dividends and share count.WACC CalculatorWeighted average cost of capital from equity, debt, their costs and the tax rate.CAPM CalculatorExpected return from the risk-free rate, beta and market return using the CAPM formula.Payback Period CalculatorPayback and discounted payback period for an investment with even or uneven cash flows.Effective Annual Rate CalculatorConvert a nominal rate to the effective annual rate (EAR / APY) for any compounding, or back.Dividend Reinvestment CalculatorProject a DRIP: portfolio value, shares and income with and without reinvesting dividends.Credit Card Payoff CalculatorSee when your card is paid off, the interest you pay, and how it compares with the minimum.Debt Snowball CalculatorPlan payoff of several debts: snowball vs. avalanche order, debt-free date and interest saved.College Savings CalculatorProject future college costs and see how much you need to save each month to pay for them.Retirement Withdrawal CalculatorSee how many years your retirement savings last with withdrawals, returns and inflation.Hourly to Salary CalculatorConvert an hourly wage to annual, monthly, biweekly, weekly and daily pay, with overtime.Bonus Tax CalculatorEstimate take-home pay on a bonus: 22% federal supplemental rate, FICA and state tax.Self-Employment Tax CalculatorCalculate Social Security and Medicare self-employment tax (15.3%) and the deductible half.Price per Square Foot CalculatorFind price per sq ft or m², total price or area, and compare several homes by value.Real Estate Commission CalculatorCalculate realtor commission, the agent and broker split, and the seller's net proceeds.Rent Split CalculatorSplit rent fairly between up to 6 roommates by room size, income or equally.Car Affordability CalculatorSee how much car you can afford with the 20/4/10 rule or your monthly budget.Daily Interest CalculatorInterest per day and total interest for any number of days, simple or compounded daily.Contribution Margin CalculatorContribution margin per unit, CM ratio, operating profit and break-even point.Customer Acquisition Cost CalculatorCAC from marketing and sales spend, plus LTV:CAC ratio and payback months.CPA CalculatorCost per acquisition from ad spend, plus break-even and target CPA from your margin.Average Order Value CalculatorAverage order value from revenue and orders, plus the revenue impact of raising AOV.Reorder Point CalculatorReorder point from daily demand, lead time and safety stock, with days until the next order.Safety Stock CalculatorSafety stock by days of cover, max − average, or service level (Z × σ × √lead time).Dimensional Weight CalculatorDIM weight and billable weight for a box in inches or cm with 139, 166, 5000 or 6000 divisors.Food Cost CalculatorPlate cost per portion, food cost percentage and menu price for any recipe.Growth Rate CalculatorTotal growth, compound growth rate per period, linear average and a projection.RPM CalculatorRevenue per 1,000 views from earnings, estimated earnings from RPM, and views for a goal.Customer Retention Rate CalculatorCustomer retention rate and churn from start, end and new customer counts.Margin to Markup CalculatorConvert gross margin % to markup % and back, with price multiplier and conversion table.Army Body Fat CalculatorArmy tape test body fat (2023 one-site or legacy method) vs AR 600-9 standards by age.Steps to Miles CalculatorConvert steps to miles and km from your height or step length, with time and calories.Swimming Pace CalculatorSwim pace per 100 m or yd, speed and splits from distance and time, plus CSS from a test.Blood Pressure CalculatorBlood pressure reading to AHA category, mean arterial pressure and pulse pressure.Waist to Height Ratio CalculatorWaist to height ratio in cm or inches with health bands and the 0.5 rule waist target.Fiber Intake CalculatorDaily fiber target from age, sex and calories (14 g per 1,000 kcal and IOM table).Alcohol Units CalculatorUK alcohol units from volume and ABV, plus a weekly total vs the 14-unit guideline.hCG Doubling Time CalculatorTwo hCG results and hours apart to doubling time and the equivalent 48-hour rise.IVF Due Date CalculatorIVF due date from a day 3, 5 or 6 embryo transfer or egg retrieval, with weeks pregnant.Baby Formula CalculatorEstimate daily and per-feed baby formula in ml and oz from weight, age and feeds.Barbell Plate CalculatorWhich plates to load on each side of the bar for any target weight, in kg or lb.Wilks CalculatorPowerlifting Wilks 2020 and DOTS scores from body weight, sex and total in kg or lb.GFR CalculatorEstimate eGFR from creatinine, age and sex with CKD-EPI 2021 and see the CKD stage.Mean Arterial Pressure CalculatorCalculate mean arterial pressure (MAP) and pulse pressure from a blood pressure reading.Cat Food CalculatorHow much wet and dry food to feed your cat per day, from weight, life stage and activity.Cat Pregnancy CalculatorFind your cat’s due date from the mating date, with a week-by-week pregnancy calendar.Sleep Debt CalculatorFind your weekly sleep debt from hours slept per night and get a simple recovery plan.Screen Time CalculatorSee your daily screen time per year and over your lifetime, and what else you could do.Book Reading Time CalculatorHow long a book takes to read from its pages or words and your reading speed.Pages per Day CalculatorHow many pages to read each day to finish a book by your date, with a reading schedule.Zakat CalculatorCalculate 2.5% zakat on cash, gold, silver and investments against the gold or silver nisab.House Flipping CalculatorFix-and-flip profit, ROI and 70% rule max offer from purchase, rehab, holding and sale costs.Airbnb Income CalculatorShort-term rental net income from nightly rate, occupancy, cleaning, fees and expenses.EV vs Gas Car Cost CalculatorCompare yearly EV charging vs gas fuel costs, cost per mile, savings and CO₂ emissions.Simplify Fractions CalculatorReduce any fraction to lowest terms with GCD steps, mixed number, decimal and equivalents.Cubic Equation SolverSolve ax³ + bx² + cx + d = 0 for real and complex roots with steps and a graph.Vector Calculator2D and 3D vectors: add, subtract, dot and cross product, magnitude, angle, unit vector, projection.Complex Number CalculatorAdd, subtract, multiply, divide complex numbers; polar form, modulus, argument, powers and roots.Summation CalculatorEvaluate sigma notation: sum any expression in n from a to b with partial sums and a chart.Arithmetic Sequence CalculatorFind the n-th term, sum and full list of an arithmetic sequence, or d from two terms.Geometric Sequence CalculatorFind the n-th term, sum and infinite sum of a geometric sequence, or r from two terms.Fibonacci CalculatorExact n-th Fibonacci number (BigInt), sequence lists, Fibonacci check and golden ratio.Pascal's Triangle GeneratorGenerate Pascal's triangle up to row 30, highlight a row and expand (ax + by)ⁿ.Binomial Distribution CalculatorBinomial probabilities P(X = k), at most, at least or between, with mean, variance and chart.Normal Distribution CalculatorNormal probabilities P(X < x), between two values and inverse percentiles, on a shaded bell curve.Poisson Distribution CalculatorPoisson probabilities for a rate λ: exactly k, at most, at least or between, with a chart.T-Test CalculatorOne-sample, two-sample (Welch/pooled) and paired t-tests with p-value and CI.Chi-Square CalculatorChi-square goodness-of-fit and independence tests with p-value and expected counts.P-Value CalculatorOne- or two-tailed p-values from z, t, chi-square or F statistics, with critical values.Variance CalculatorSample and population variance and standard deviation with a step-by-step deviations table.Five Number Summary CalculatorMin, Q1, median, Q3, max, IQR and fences of a data set, with a box plot.Outlier CalculatorFind outliers with 1.5×/3× IQR fences, z-scores or modified z-scores; get the cleaned data.Geometric Mean CalculatorGeometric, harmonic, arithmetic and quadratic means compared, or average growth from % changes.Expected Value CalculatorExpected value, variance and standard deviation from outcomes and their probabilities.Trigonometry CalculatorSin, cos, tan, csc, sec, cot and inverses in degrees or radians, with exact values.Arc Length CalculatorArc length, sector area and chord from radius and angle, or solve for the radius or angle.Cylinder Volume CalculatorCylinder volume in liters, gallons and cubic units from radius or diameter, plus surface area.Regular Polygon CalculatorArea, perimeter, apothem, radius and angles of a regular polygon from any one measurement.Factors CalculatorAll factors and factor pairs of a number, prime factors, divisor count and perfect check.Big Number CalculatorExact + − × ÷ mod and powers for huge integers with hundreds of digits, plus digit count.RC Time Constant Calculatorτ = RC, charge % at 1-5τ, and capacitor charge or discharge voltage at any time t.Resonant Frequency CalculatorLC resonant frequency f = 1/(2π√LC), or solve the inductance or capacitance you need.Capacitor Series and Parallel CalculatorTotal capacitance of capacitors in series or parallel, plus stored energy ½CV² and charge.Three-Phase Power CalculatorkW, kVA and kVAR from volts, amps and power factor, or three-phase current from kW or kVA.Generator Size CalculatorAdd appliance running and starting watts to find the generator size you need.Pressure CalculatorSolve P = F/A for pressure, force or area in Pa, kPa, bar, psi and atm.Work CalculatorSolve W = F·d·cos θ for work, force, distance or angle in J, kWh and ft-lb.Hooke's Law CalculatorSolve F = kx for spring force, spring constant or extension, plus stored spring energy.Centripetal Force CalculatorCentripetal force and acceleration from mass, radius and speed or RPM: F = mv²/r.Gravitational Force CalculatorNewton's law of gravitation F = Gm₁m₂/r² for any two masses, with planet presets.Speed of Sound CalculatorSpeed of sound from air temperature or medium, and distance from an echo or thunder delay.Doppler Effect CalculatorObserved frequency from source and observer speeds, or source speed from a pitch shift.Specific Heat CalculatorSolve Q = mcΔT for heat energy, mass, specific heat or temperature change, with materials.Percent Yield CalculatorPercent yield from actual and theoretical yield, or theoretical yield from moles and formulas.PPM CalculatorConvert ppm to mg/L, %, ppb and mg/kg, find ppm of a solution, or ppm to mg/m³ for gases.Grams to Moles CalculatorConvert grams to moles and back from a chemical formula, with molar mass and atom counts.Decibel CalculatorAdd dB levels, convert power or voltage ratios to dB, and find sound level at a distance.Pipe Flow Rate CalculatorFlow rate from pipe diameter and velocity (GPM, L/s, m³/h), velocity from flow, or pipe size.Stud CalculatorCount wall studs and plates from wall length, spacing, corners and openings.Carpet CalculatorCarpet for your rooms in sq ft and sq yd from a 12 or 15 ft roll, with padding and cost.Baseboard CalculatorLinear feet of baseboard and number of pieces for your rooms, minus doorways.Grout CalculatorGrout in kg, lb and bags from tile size, joint width, depth and area.Rebar CalculatorRebar for a slab grid: bars each way, total length, weight by bar size and stock bars.Asphalt CalculatorTons of asphalt from area and thickness at 145 lb/ft³, with volume and cost.Sand CalculatorSand in cubic yards, m³, tons and bags for any area and depth.Retaining Wall CalculatorBlocks, caps, base gravel and drainage stone for a block retaining wall.Siding CalculatorSiding squares, panels and J-channel from walls and gables minus doors and windows.Pool Chlorine CalculatorHow much liquid chlorine, bleach or shock to add to reach a target free chlorine.Aquarium Volume CalculatorFish tank gallons, liters and water weight: rectangle, cylinder, bow-front and hexagon tanks.Fertilizer CalculatorPounds of fertilizer and bags for your lawn from N-P-K and a target rate per 1,000 sq ft.Raised Bed Soil CalculatorSoil for raised garden beds in cubic feet, cubic yards, liters and bags, with mix recipes.Plant Spacing CalculatorHow many plants fit an area at a given spacing, in a square, triangular or row pattern.LED Savings CalculatorYearly savings, kWh saved and payback time when switching old bulbs to LED.Tank Volume CalculatorTotal and filled volume of cylinder, rectangular and capsule tanks in gallons and liters.Rainwater Harvesting CalculatorGallons or liters of rainwater a roof collects from its area, rainfall and surface.Quarter Mile CalculatorEstimate 1/4 mile ET and trap speed from horsepower and weight, or HP from a time slip.Compression Ratio CalculatorStatic engine compression ratio from bore, stroke, chamber, gasket, deck and piston volume.Concrete Steps CalculatorConcrete volume and bags for poured steps from step count, rise, run, width and landing.Weighted Grade CalculatorCurrent class grade from weighted categories, plus the score you need on the final.SGPA to CGPA CalculatorCGPA from semester SGPAs and credits, with percentage by ×9.5, ×10 or VTU formula.GPA to Percentage CalculatorConvert a 4.0, 5.0 or 10-point GPA to a percentage and back with common formulas.Meat per Person CalculatorHow much raw meat to buy for a party or BBQ from guests, meat type and appetite.Rice to Water Ratio CalculatorExact water and cook time for any rice in cups or grams: stovetop, rice cooker or Instant Pot.Yeast ConverterConvert fresh, active dry, instant yeast and sourdough starter by grams, teaspoons or packets.Butter ConverterConvert butter between sticks, cups, tablespoons, grams, ounces and 250 g EU blocks.Cake Servings CalculatorHow many wedding or party slices a round, square or sheet cake serves, tier by tier.Fabric Yardage CalculatorHow many yards or meters of fabric to buy for your pieces, width, seams and pattern repeat.Depth of Field CalculatorNear and far focus limits, depth of field and hyperfocal distance for any camera or lens.Crop Factor CalculatorCrop factor, full-frame equivalent focal length and aperture, and field of view for any sensor.Print Size CalculatorPrint size from pixels and DPI, max print size by megapixels, and pixels needed for any print.3D Printing Cost CalculatorCost and selling price of a 3D print: filament, power, machine wear, failures and labor.