Simplify Your Workflow: Search MiniWebtool.
Add Extension
Home Page > Math > Geometry Calculators > Circle Calculator

Circle Calculator

Calculate radius, diameter, circumference, and area of a circle from any single value. Includes arc length, sector area, chord length, and segment area calculations with step-by-step solutions and interactive diagram.

Circle Calculator

Try these examples:

r = 5 d = 10 C = 31.42 r = 7, θ = 90°
📐 Arc, Sector & Segment (Optional)

Enter an angle to calculate arc length, sector area, chord length, and segment area.

Embed Circle Calculator Widget

About Circle Calculator

Welcome to the Circle Calculator, a comprehensive geometry tool that calculates all properties of a circle from any single known measurement. Enter the radius, diameter, circumference, or area, and instantly get all other values plus optional arc length, sector area, and segment area calculations. Results are displayed in both decimal and exact π notation for maximum precision.

What is a Circle?

A circle is a two-dimensional shape consisting of all points in a plane that are equidistant from a central point called the center. This constant distance from the center to any point on the circle is called the radius. Circles are fundamental shapes in mathematics, appearing throughout nature, engineering, and everyday life.

Circle Formulas

Basic Relationships

Diameter from Radius
$$d = 2r$$
Radius from Diameter
$$r = \frac{d}{2}$$

Circumference (Perimeter)

The circumference is the distance around the circle:

Circumference Formula
$$C = 2\pi r = \pi d$$

Area

The area is the space enclosed by the circle:

Area Formula
$$A = \pi r^2 = \frac{\pi d^2}{4}$$

Advanced Circle Calculations

Arc Length

An arc is a portion of the circumference. Given a central angle θ:

Arc Length Formula
$$L_{arc} = \frac{\theta}{360°} \times 2\pi r = \frac{\theta \pi r}{180}$$

Sector Area

A sector is a "pie slice" of the circle bounded by two radii and an arc:

Sector Area Formula
$$A_{sector} = \frac{\theta}{360°} \times \pi r^2 = \frac{\theta \pi r^2}{360}$$

Chord Length

A chord is a straight line connecting two points on the circle:

Chord Length Formula
$$c = 2r \sin\left(\frac{\theta}{2}\right)$$

Segment Area

A segment is the region between a chord and its arc:

Segment Area Formula
$$A_{segment} = A_{sector} - A_{triangle} = \frac{r^2}{2}\left(\frac{\theta \pi}{180} - \sin\theta\right)$$

How to Use This Calculator

  1. Select what you know: Choose Radius, Diameter, Circumference, or Area from the dropdown
  2. Enter your value: Input the known measurement
  3. Choose a unit (optional): Select from mm, cm, m, km, in, ft, yd, or mi
  4. Add an angle (optional): Enter a central angle in degrees to calculate arc length, sector area, chord length, and segment area
  5. Click Calculate: View all circle properties with both decimal and π notation, plus an interactive diagram

Understanding π (Pi)

Pi (π) is the ratio of a circle's circumference to its diameter. It is an irrational number, meaning its decimal representation never ends and never repeats:

π ≈ 3.14159265358979323846...

Common approximations include 3.14159 or 22/7. This calculator uses high-precision arithmetic and shows results in exact π notation when possible.

Real-World Applications

🍕
Pizza Sizing
12" pizza = 113 in² area
🚗
Tire Diameter
26" wheel = 81.7" circumference
🏊
Pool Covers
18ft diameter = 254 ft² area
🎯
Dart Board
17.75" diameter = 247 in² area

Circle Properties Summary

PropertySymbolFormulaDescription
Radiusrd/2 or C/(2π)Distance from center to edge
Diameterd2rDistance across through center
CircumferenceC2πr or πdPerimeter (distance around)
AreaAπr²Space enclosed by the circle
Arc LengthLθπr/180°Length of a portion of circumference
Sector AreaAsθπr²/360°Area of a "pie slice"
Chord Lengthc2r·sin(θ/2)Straight line between two points on circle
Segment AreaAsegSector - TriangleArea between chord and arc

Frequently Asked Questions

What is the formula for the area of a circle?

The area of a circle is calculated using the formula A = πr², where r is the radius. For example, a circle with radius 5 units has an area of π × 5² = 25π ≈ 78.54 square units. Alternatively, using the diameter d, the formula is A = π(d/2)² = πd²/4.

How do you calculate the circumference of a circle?

The circumference (perimeter) of a circle is calculated using C = 2πr or C = πd, where r is the radius and d is the diameter. For example, a circle with radius 7 units has a circumference of 2 × π × 7 = 14π ≈ 43.98 units.

What is the relationship between radius and diameter?

The diameter of a circle is exactly twice the radius. Expressed as formulas: d = 2r and r = d/2. The radius is the distance from the center to any point on the circle, while the diameter is the distance across the circle through its center.

What is arc length and how is it calculated?

Arc length is the distance along the curved line of a circle between two points. It is calculated using the formula: Arc Length = (θ/360°) × 2πr, where θ is the central angle in degrees and r is the radius. Alternatively, in radians: Arc Length = θ × r.

What is the difference between a sector and a segment of a circle?

A sector is a "pie slice" of a circle bounded by two radii and an arc. A segment is the region between a chord and its arc. Sector area = (θ/360°) × πr². Segment area = Sector area - Triangle area, where the triangle is formed by the two radii and the chord.

What is the value of π (pi)?

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. Its value is approximately 3.14159265358979... and it is an irrational number, meaning its decimal representation never ends and never repeats. For calculations, π ≈ 3.14159 or 22/7 are common approximations.

Additional Resources

Reference this content, page, or tool as:

"Circle Calculator" at https://MiniWebtool.com/circle-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Feb 01, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Related MiniWebtools:

Area of a Circle Calculator
Area of a Parallelogram Calculator
Area of A Sector Calculator
Area of Equilateral Triangle Calculator
Circumscribed Circle (Circumcircle) CalculatorNew
Ellipse Circumference Calculator
Equation of a Line CalculatorNew
Frustum CalculatorNew
General Triangle Solver
Great Circle Distance CalculatorNew

Geometry Calculators:

Top & Updated:

Random PickerRandom Name PickerLine CounterBatting Average CalculatorFPS ConverterRelative Standard Deviation CalculatorSort NumbersInstagram User ID LookupMAC Address GeneratorRemove SpacesERA CalculatorJob FinderWord to Phone Number ConverterFeet and Inches to Cm ConverterMAC Address LookupFacebook User ID LookupRandom Truth or Dare GeneratorSum CalculatorOPS CalculatorPercent Off CalculatorSquare Root (√) CalculatorLog Base 10 CalculatorSHA256 Hash GeneratorBitwise CalculatorNumber of Digits CalculatorPhone Number ExtractorImage ResizerVertical Jump CalculatorSlope and Grade CalculatorMP3 LooperOn Base Percentage CalculatorSalary Conversion CalculatorAudio SplitterRoman Numerals ConverterRandom IMEI GeneratorRandom Letter GeneratorRandom Quote GeneratorSlugging Percentage CalculatorNumber to Word ConverterAI Text HumanizerRandom Poker Hand GeneratorCaffeine Overdose CalculatorRandom Loadout GeneratorRandom Activity GeneratorSun, Moon & Rising Sign Calculator 🌞🌙✨Decimal to BCD ConverterRandom Movie PickerMerge VideosSaturn Return CalculatorCm to Feet and Inches ConverterBCD to Decimal ConverterRandom Fake Address GeneratorWAR CalculatorText FormatterVideo to Image ExtractorBinary to Gray Code ConverterCompound Growth CalculatorOctal CalculatorInvisible Text GeneratorTime Duration CalculatorRandom Writing Prompt GeneratorFile Size ConverterLove Compatibility CalculatorRandom Credit Card GeneratorFirst n Digits of PiMaster Number CalculatorWHIP CalculatorQuotient and Remainder CalculatorGrade Calculator⬛ Aspect Ratio CalculatorSteel Weight CalculatorRandom Time GeneratorAdd Prefix and Suffix to TextImage CompressorRemove AccentCompare Two StringsRandom Sound Frequency GeneratorYouTube Channel StatisticsDay of Year CalendarPercent Growth Rate CalculatorWord Ladder GeneratorRandom Superpower GeneratorRandom Object GeneratorBaby Growth Percentile CalculatorOutlier CalculatorCM to Inches ConverterClothing Size ConverterName Number CalculatorBreak Line by CharactersAdd Text to ImageGray Code to Binary ConverterBattery Life CalculatorRandom Number PickerRandom Birthday GeneratorSHA512 Hash GeneratorLeap Years ListIP Subnet CalculatorArc Length CalculatorSum of Positive Integers CalculatorEmail ExtractorURL ExtractorAI ParaphraserAI Punctuation AdderList of Prime NumbersDay of the Year Calculator - What Day of the Year Is It Today?Video CompressorBinary to BCD ConverterIP Address to Hex ConverterSort Lines AlphabeticallyHex to BCD ConverterBCD to Binary ConverterLottery Number GeneratorBCD to Hex ConverterMedian CalculatorStandard Error CalculatorList RandomizerAverage CalculatorModulo CalculatorPVIFA CalculatorReverse VideoHypotenuse CalculatorRemove Audio from VideoActual Cash Value CalculatorScientific Notation to Decimal ConverterNumber ExtractorAngel Number CalculatorLog Base 2 CalculatorRoot Mean Square CalculatorSHA3-256 Hash GeneratorAI Sentence Expander📅 Date CalculatorLbs to Kg ConverterHex to Decimal ConverterRandom Group GeneratorConvolution CalculatorMAC Address AnalyzerRandom String GeneratorRemove Leading Trailing SpacesAmortization CalculatorMarkup CalculatorPVIF CalculatorDecimal to Hex ConverterInstagram Font GeneratorSocial Media Image Size GuideTikTok Money CalculatorTwitter/X Character CounterTwitter/X Timestamp ConverterYouTube Watch Time CalculatorTwitch Earnings CalculatorYouTube Shorts Monetization CalculatorFacebook Ad Cost CalculatorSocial Media ROI CalculatorSocial Media Post Time OptimizerSocial Media Username CheckerCTR CalculatorROAS CalculatorInfluencer ROI CalculatorForce CalculatorAcceleration CalculatorVelocity CalculatorMomentum CalculatorProjectile Motion CalculatorKinetic Energy CalculatorPotential Energy CalculatorWork and Power CalculatorDensity CalculatorPressure CalculatorIdeal Gas Law CalculatorFree Fall CalculatorTorque CalculatorHorsepower CalculatorDilution CalculatorChemical Equation BalancerStoichiometry CalculatorPercent Yield CalculatorEmpirical Formula CalculatorBoiling Point CalculatorTitration CalculatorMole/Gram/Particle ConverterIrregular Polygon Area CalculatorFrustum CalculatorTorus Calculator3D Distance CalculatorGreat Circle Distance CalculatorCircumscribed Circle (Circumcircle) CalculatorInscribed Circle (Incircle) CalculatorAngle Bisector CalculatorTangent Line to Circle CalculatorHeron's Formula CalculatorCoordinate Geometry Distance CalculatorVolume of Revolution CalculatorSurface of Revolution CalculatorParametric Curve GrapherRiemann Sum CalculatorTrapezoidal Rule CalculatorSimpson's Rule CalculatorImproper Integral CalculatorL'Hôpital's Rule CalculatorMaclaurin Series CalculatorPower Series CalculatorSeries Convergence Test CalculatorInfinite Series Sum CalculatorAverage Rate of Change CalculatorInstantaneous Rate of Change CalculatorRelated Rates SolverOptimization Calculator (Calculus)Gradient Calculator (Multivariable)Divergence CalculatorCurl CalculatorLine Integral CalculatorSurface Integral CalculatorJacobian Matrix CalculatorNewton's Method CalculatorRREF Calculator (Row Echelon Form)Matrix Inverse CalculatorMatrix Multiplication CalculatorDot Product CalculatorCross Product CalculatorVector Magnitude CalculatorUnit Vector CalculatorAngle Between Vectors CalculatorNull Space CalculatorColumn Space CalculatorCramer's Rule CalculatorMatrix Diagonalization CalculatorQR Decomposition CalculatorCholesky Decomposition CalculatorMatrix Power CalculatorCharacteristic Polynomial CalculatorBayes' Theorem CalculatorF-Test / F-Distribution CalculatorHypergeometric Distribution CalculatorNegative Binomial Distribution CalculatorGeometric Distribution CalculatorExponential Distribution CalculatorWeibull Distribution CalculatorBeta Distribution CalculatorSpearman Rank Correlation CalculatorFisher's Exact Test CalculatorContingency Table CalculatorOdds Ratio CalculatorRelative Risk CalculatorEffect Size CalculatorPermutations with Repetition CalculatorModular Exponentiation CalculatorPrimitive Root CalculatorPerfect Number CheckerAmicable Number CheckerTwin Prime FinderMersenne Prime CheckerGoldbach Conjecture VerifierMöbius Function CalculatorEgyptian Fraction CalculatorFibonacci Number CheckerDigital Root CalculatorPartition Function CalculatorBoolean Algebra SimplifierKarnaugh Map (K-Map) SolverLogic Gate SimulatorGraph Coloring CalculatorTopological Sort CalculatorAdjacency Matrix CalculatorRecurrence Relation SolverInclusion-Exclusion CalculatorLinear Programming SolverTraveling Salesman Solver (TSP)Hamiltonian Path CheckerPlanar Graph CheckerNetwork Flow Calculator (Max Flow)Stable Marriage Problem SolverFirst-Order ODE SolverSecond-Order ODE SolverDirection Field / Slope Field PlotterEuler's Method CalculatorBernoulli ODE SolverSystem of ODEs SolverGroup Theory Order CalculatorRing and Field CalculatorJordan Normal Form CalculatorMatrix Exponential CalculatorTensor Product CalculatorFast Fourier Transform (FFT) CalculatorZ-Transform CalculatorNumerical Integration CalculatorTOML to JSON ConverterJSON to CSV ConverterXML to JSON ConverterSQL to MongoDB Query ConverterCSS Flexbox PlaygroundCSS Grid GeneratorJWT GeneratorBcrypt Hash Generator / CheckerColor Code Converter (All Formats)Git Command Generator.env File GeneratorLorem Picsum / Placeholder Image GeneratorText to Binary/Hex/ASCII ConverterSyllable CounterSentence CounterParagraph CounterSpeaking Time CalculatorReading Time CalculatorWhitespace VisualizerStrikethrough Text GeneratorTorque Converter (Nm, ft-lb, kgf-cm)Data Transfer Rate ConverterFuel Efficiency ConverterAstronomical Unit ConverterRing Size ConverterPaper Size ReferenceGas Mileage CalculatorEV Range CalculatorEV Charging Time Calculator0–60 / Quarter Mile CalculatorCar Lease CalculatorVehicle Towing Capacity CalculatorExposure Triangle CalculatorCrop Factor CalculatorMegapixel to Print Size CalculatorPhoto File Size EstimatorMusic BPM TapperMusic Key TransposerVideo Bitrate CalculatorSeed Germination Rate CalculatorFertilizer Calculator (NPK)Raised Bed Soil CalculatorFrost Date CalculatorLawn Fertilizer CalculatorCompost Calculator (C:N Ratio)Solar Panel CalculatorSolar ROI CalculatorHome Energy Audit CalculatorAppliance Energy Cost CalculatorWater Usage CalculatorElectricity Generation Cost CalculatorHeat Loss CalculatorFlight Distance CalculatorTravel Budget CalculatorJet Lag CalculatorPacking List GeneratorTip Splitter (Advanced)Lease vs Buy CalculatorHourly Rate Calculator (Freelancer)Invoice Late Fee CalculatorESPP CalculatorStock Split CalculatorOptions Probability CalculatorDollar to Gold ConverterBeam Load CalculatorPipe Flow CalculatorBolt Torque CalculatorGravel, Sand & Topsoil CalculatorRandom Sentence GeneratorRandom Paragraph GeneratorRandom Math Problem GeneratorRandom Bible Verse GeneratorRandom Cat/Dog Name GeneratorRandom Debate Topic GeneratorBody Recomposition CalculatorAlcohol Calorie CalculatorMedication Dosage CalculatorPace to Calories CalculatorHydration CalculatorTrain Meeting Problem SolverAge Word Problem SolverMixture Problem SolverWork Rate Problem SolverDistance-Speed-Time Triangle CalculatorCoin Word Problem SolverNumber Bonds GeneratorCarry and Borrow VisualizerTimes Tables QuizMental Math TrainerRoman Numeral Math SolverEgyptian Multiplication CalculatorVedic Math Tricks CalculatorRussian Peasant MultiplicationSoroban Abacus SimulatorAnnuity Payout CalculatorReverse Mortgage CalculatorVariable Annuity CalculatorFixed Indexed Annuity CalculatorBond Convexity CalculatorBond Duration Calculator (Macaulay & Modified)Forward Rate CalculatorMortgage Recast CalculatorTreasury Inflation-Protected Securities (TIPS) CalculatorStock Beta CalculatorTreynor Ratio CalculatorSortino Ratio CalculatorDoppler Effect CalculatorSpring Constant CalculatorPendulum Period CalculatorCentripetal Force CalculatorAngular Velocity CalculatorMoment of Inertia CalculatorSnell's Law CalculatorCoulomb's Law CalculatorElectric Field CalculatorMagnetic Field of Wire CalculatorLens Equation CalculatorA/B Test Significance CalculatorA/B Test Sample Size CalculatorConversion Rate CalculatorCustomer Lifetime Value (CLV) CalculatorCustomer Acquisition Cost (CAC) CalculatorChurn Rate CalculatorRetention Rate Cohort CalculatorNPS (Net Promoter Score) CalculatorPareto Chart GeneratorSix Sigma Process Capability CalculatorTessellation GeneratorSpirograph GeneratorVoronoi Diagram GeneratorDelaunay Triangulation GeneratorL-System Fractal GeneratorMandelbrot Set ExplorerJulia Set GeneratorPolar Equation Plotter3D Surface PlotterSierpinski Triangle GeneratorcURL Command BuilderHTTP Status Code Reference