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

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
Cone Flat Pattern (Template) GeneratorNew
Ellipse Circumference Calculator
Euler Characteristic CalculatorNew
Polygon Diagonals CalculatorNew
Pythagorean Theorem Calculator
Shoelace Formula CalculatorNew
Surface Area Calculator
Triangle Centroid CalculatorNew

Geometry Calculators:

Top & Updated:

Random Name PickerRandom PickerRelative Standard Deviation CalculatorFPS ConverterSort NumbersLine CounterBatting Average CalculatorMAC Address GeneratorRemove SpacesSaturn Return CalculatorInstagram User ID LookupMAC Address LookupFeet and Inches to Cm ConverterWord to Phone Number ConverterFirst n Digits of PiERA CalculatorPercent Off CalculatorFacebook User ID LookupSum CalculatorRandom Quote GeneratorSHA256 Hash GeneratorRandom Group GeneratorLog Base 10 CalculatorRandom Truth or Dare GeneratorBitwise CalculatorNumber of Digits CalculatorSquare Root (√) CalculatorPhone Number ExtractorTwitter/X Timestamp ConverterRoman Numerals ConverterRandom Superpower GeneratorCm to Feet and Inches ConverterOn Base Percentage CalculatorSlugging Percentage CalculatorSalary Conversion CalculatorYouTube Thumbnail DownloaderAI ParaphraserMP3 LooperQuotient and Remainder CalculatorRandom IMEI GeneratorMaster Number CalculatorImage SplitterOutlier CalculatorVideo to Image ExtractorAI Text HumanizerLove Compatibility CalculatorBinary to Gray Code ConverterVertical Jump CalculatorOPS CalculatorYouTube Earnings EstimatorDecimal to BCD ConverterSun, Moon & Rising Sign Calculator 🌞🌙✨Number to Word ConverterBCD to Decimal ConverterAI Punctuation AdderPER CalculatorOne Rep Max (1RM) CalculatorModulo CalculatorCompare Two StringsTime Duration CalculatorAudio SplitterRemove AccentCompound Growth CalculatorRandom Activity GeneratorNumber ExtractorStandard Error CalculatorVideo CompressorDay of Year CalendarRandom Number PickerGray Code to Binary ConverterMerge VideosOctal CalculatorShort Selling Profit CalculatorSocial Media Username CheckerRandom Birthday GeneratorIP Address to Hex ConverterRandom Emoji GeneratorMartingale Strategy CalculatorMercury Retrograde CalendarExponential Decay CalculatorAdd Prefix and Suffix to TextRandom Movie PickerReverse VideoRandom Poker Hand GeneratorBinary to BCD ConverterDay of the Year Calculator - What Day of the Year Is It Today?Percent Growth Rate CalculatorRandom Time GeneratorCM to Inches ConverterRandom Coordinate GeneratorRandom Fake Address GeneratorMAC Address AnalyzerName Number CalculatorConvolution CalculatorFirst n Digits of eSlope and Grade CalculatorSHA512 Hash GeneratorList of Prime NumbersRemove Lines Containing...Log Base 2 CalculatorText FormatterEmail ExtractorURL ExtractorWHIP CalculatorSort Lines AlphabeticallyHex to BCD ConverterBCD to Binary ConverterLottery Number GeneratorBCD to Hex ConverterMedian CalculatorLeap Years ListList RandomizerBreak Line by CharactersAverage CalculatorPVIFA CalculatorWAR CalculatorHypotenuse CalculatorRemove Audio from VideoActual Cash Value CalculatorScientific Notation to Decimal ConverterAngel Number CalculatorRoot Mean Square CalculatorSum of Positive Integers CalculatorSHA3-256 Hash GeneratorAI Sentence Expander📅 Date CalculatorLbs to Kg ConverterHex to Decimal ConverterRandom String GeneratorRemove Leading Trailing SpacesAmortization CalculatorMarkup CalculatorPVIF CalculatorDecimal to Hex ConverterDaily Time Savings CalculatorLorem Ipsum GeneratorReadability Score CalculatorKeyword Density CheckerBionic Reading ConverterText to Speech ReaderFancy Text GeneratorZalgo Text GeneratorUpside Down Text GeneratorInvisible Text GeneratorASCII Art GeneratorList Difference CalculatorText Column ExtractorText to SQL List ConverterInvisible Character RemoverStock Average CalculatorPosition Size CalculatorMargin Call CalculatorFutoshiki GeneratorHashi (Bridges) Puzzle GeneratorSlitherlink Puzzle GeneratorWord Search Puzzle GeneratorCrossword Puzzle MakerCryptogram GeneratorWord Scramble GeneratorWord Ladder GeneratorBingo Card GeneratorConnect the Dots GeneratorTip CalculatorCurrency Converter401(k) CalculatorRoth IRA CalculatorRetirement CalculatorSocial Security Benefits CalculatorPension CalculatorRMD CalculatorSIP CalculatorMutual Fund CalculatorStock Profit Loss CalculatorDividend Reinvestment CalculatorDollar Cost Averaging CalculatorBusiness Loan CalculatorPersonal Loan CalculatorDebt Payoff CalculatorDebt Consolidation CalculatorNet Worth CalculatorBudget CalculatorSavings Goal CalculatorEmergency Fund CalculatorMortgage Payoff CalculatorDown Payment CalculatorFHA Loan CalculatorHELOC CalculatorBreak-Even CalculatorBusiness Valuation CalculatorEmployee Cost CalculatorCrypto Profit/Loss CalculatorBitcoin Investment CalculatorIncome Tax CalculatorTax Bracket CalculatorTax Refund EstimatorCapital Gains Tax CalculatorSelf-Employment Tax Calculator1099 Tax CalculatorW-4 Withholding CalculatorProperty Tax CalculatorEstate Tax CalculatorChild Support CalculatorAlimony CalculatorTax-Equivalent Yield CalculatorRent vs Buy CalculatorRental Property CalculatorClosing Costs CalculatorReal Estate Commission CalculatorHouse Flipping Profit CalculatorHome Equity CalculatorIdeal Weight CalculatorBAC CalculatorProtein Intake CalculatorKeto CalculatorIntermittent Fasting CalculatorWeight Loss CalculatorGFR CalculatorCreatinine Clearance CalculatorBlood Pressure InterpreterHeight Percentile CalculatorLife Expectancy CalculatorBiological Age CalculatorBlood Type CalculatorBody Type CalculatorLean Body Mass CalculatorCarbohydrate CalculatorNet Carbs CalculatorHeart Disease Risk CalculatorCycling Speed CalculatorSwimming Pace CalculatorSteps to Distance CalculatorArmy Body Fat CalculatorStrength Standards CalculatorMarathon Pace CalculatorTriathlon Pace CalculatorBowling Score CalculatorGolf Handicap CalculatorPace Zone CalculatorPregnancy Weight Gain CalculatorBaby Growth Percentile CalculatorBreastfeeding Calorie CalculatorGestational Age CalculatorPregnancy Calorie CalculatorRecipe ScalerCooking Unit ConverterRecipe Nutrition CalculatorCups to Grams ConverterMeat Smoking CalculatorTurkey Cooking Time CalculatorPizza Dough CalculatorSourdough CalculatorSous Vide CalculatorAir Fryer ConverterButter to Oil ConverterFresh to Dried Herb ConverterDog Food CalculatorMultiple Fraction CalculatorPuppy Weight PredictorChocolate Toxicity CalculatorDog Pregnancy CalculatorRaw Feeding CalculatorPet Insurance CalculatorDog Life Expectancy CalculatorJSON Formatter/ValidatorRegex TesterDiff CheckerJavaScript Minifier/BeautifierCSS BeautifierHTML BeautifierYAML Formatter/ValidatorCSV to JSON ConverterMarkdown EditorHTML to Markdown ConverterImage to Base64 ConverterCSS Box Shadow GeneratorIP Subnet CalculatorAPI TesterASCII Table ReferenceWebhook TesterSchema Markup GeneratorRobots.txt GeneratorXML Sitemap GeneratorOpen Graph CheckerDomain Age CheckerWHOIS LookupDNS LookupHeadline AnalyzerPage Speed CheckerRedirect CheckerHreflang Tag GeneratorDomain Trust CheckerBroken Link CheckerAI Content DetectorAI Blog Title GeneratorAI Email WriterAI Hashtag GeneratorAI Slogan GeneratorAI Article Outline GeneratorAI Token CounterInstagram Engagement Rate CalculatorTikTok Engagement Rate CalculatorYouTube Tag ExtractorYouTube Comment PickerInstagram Font GeneratorSocial Media Image Size GuideTikTok Money CalculatorYouTube Channel StatisticsTwitter/X Character CounterYouTube Watch Time CalculatorTwitch Earnings CalculatorYouTube Shorts Monetization CalculatorFacebook Ad Cost CalculatorSocial Media ROI CalculatorSocial Media Post Time OptimizerCTR 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 ConverterLED Resistor CalculatorVoltage Divider CalculatorParallel Resistor CalculatorCapacitor Calculator555 Timer CalculatorWire Gauge CalculatorTransformer CalculatorRC Time Constant CalculatorPower Factor CalculatorDecibel (dB) CalculatorImpedance CalculatorResonant Frequency CalculatorGrade CalculatorFinal Grade CalculatorWeighted Grade CalculatorTest Score CalculatorSignificant Figures CalculatorStudy Timer (Pomodoro)Long Division CalculatorRounding CalculatorCompleting the Square CalculatorRatio Calculatorp-Value CalculatorNormal Distribution CalculatorPercentile CalculatorFive Number Summary CalculatorCross Multiplication Calculator