Z SCORE TABLE
  • Z Table
    • Z Scores to Percentiles Chart
    • Z Score Calculator
    • Z Score Probability Calculator
    • Interactive Z Table
    • Z Score Formula
    • How to calculate the z score
    • How To Use Z-Score Table
    • Calculate Z-score
    • Parameters in Statistics
    • Z Score Chart Basics
    • History of Normal Distirbution
    • Statistics Z Score Jokes
    • When to Use Z Test vs T Test
    • Z Score Practice Problems
    • Confidence Interval Calculator >
      • Confidence Interval in Excel
      • 90 confidence interval z score
      • 95 Confidence Interval Z Score
      • 99 Confidence Interval Z Score
    • Z Score Confidence Interval
  • Statistics
    • Statistics Symbols
    • Statistics Formulas >
      • Binomial Coefficient
      • Empirical Rule
      • Correlation Coefficient
    • P Value Calculator >
      • P Value Calculator from Z Score
      • P Value Calculator from T Score
      • P Value Calculator from Chi-Square
      • P Value Calculator from F Ratio (ANOVA)
      • P Value Calculator from Pearson R
      • P Value Calculator Tukey's Q Score
    • Cumulative Binomial Probability Calculator
    • Interquartile Range Calculator
    • Empirical Rule Calculator
    • Mean, Median and Mode Calculator
    • Sample Size Calculator
    • Other Statistical Tables >
      • T Value Table
      • Chi-Square Table
      • F Distribution Table
    • Standard Deviation Calculator
    • Normal vs Non-Normal Distribution: Understanding the Differences
    • Explanatory Variable: Understanding Its Role in Statistical Analysis
    • Independent variable vs dependent
    • Statistics Forum
  • Math
    • Combination Calculator
    • Permutation Calculator
    • Exploring 7 Unsolvable Math Problems >
      • Riemann Hypothesis
    • Math Problems >
      • Math Problems for 1st Graders
      • Math Problems for 2nd Graders
      • Math Problems for 3rd Graders
      • Math Problems for 4th Graders
      • Math Problems for 5th Graders
      • Math Problems for 6th Graders
      • Math Problems for 7th Graders
      • Math Problems for 8th Graders
      • Math Problems for 9th Graders
      • Math Problems for 10th Graders
      • Math Problems for 11th Graders
    • Times Tables >
      • 1 Times Table
      • 2 Times Table
      • 3 Times Table
      • 4 Times Table
      • 5 Times Table
      • 6 Times Table
      • 7 Times Table
      • 8 Times Table
      • 9 Times Table
      • 10 Times Table
    • Multiplication Tables >
      • Multiplication Table by 20
      • Multiplication Table by 19
      • Multiplication Table by 18
      • Multiplication Table by 17
      • Multiplication Table by 16
      • Multiplication Table by 15
      • Multiplication Table by 14
      • Multiplication Table by 13
      • Multiplication Table by 12
      • Multiplication Table by 11
      • Multiplication Table by 10
      • Multiplication Table by 9
      • Multiplication Table by 8
      • Multiplication Table by 7
      • Multiplication Table by 6
      • Multiplication Table by 5
      • Multiplication Table by 4
      • Multiplication Table by 3
    • Roman Numerals >
      • Roman Numerals Chart
      • Roman Numerals Converter
      • I Roman Numerals
      • II Roman Numerals
      • III Roman Numerals
      • IV Roman Numerals
      • V Roman Numerals
      • VI Roman Numerals
      • VII Roman Numerals
      • VIII Roman Numerals
      • IX Roman Numerals
      • X Roman Numerals
      • XI Roman Numerals
      • XII Roman Numerals
      • XIII Roman Numerals
      • XIV Roman Numerals
      • XV Roman Numerals
      • XVI Roman Numerals
      • XVII Roman Numerals
      • XLVI Roman Numerals >
        • TEMP XVII Roman Numerals
    • Percentage Increase Calculator
    • Linear Equations >
      • Two-Variable Linear Equations Test with Answers
      • One Variable Linear Equations >
        • Ax=B Linear Equation Calculator
        • Ax=B Linear Equation Practice Test
    • Decimal Places Value Chart
    • Cone Volume Calculator
    • Rounding Calculator >
      • Round 15 to the nearest ten
      • Round 75 to the nearest ten
      • Round 35 to the nearest ten
      • Round 5 to the nearest ten
      • Round 3 to the Nearest Ten
    • Factor Calculator >
      • Factor of 36
      • Factor of 30
      • Factor of 32
      • Factor of 35
      • Factor of 39
      • Factor of 33
      • Factor of 34
      • Factor of 3
      • Factor of 3/4
      • Factor of 38
    • Radius of a Circle
    • Fraction Calculator
    • Random Number Generator
    • Horizontal Line
    • X and Y Axis
    • Root Calculator
    • Square Root Calculator >
      • Square root of 2
      • Square root of 8
      • Square root of 5
      • Square root of 4
      • Square root of 3
      • Square root of 64
      • Square root of 10
      • Square root of 16
      • Square root of 25
      • Square root of 12
      • Square root of 50
      • Square root of 20
      • Square root of 9
      • Square root of 100
      • Square root of 36
      • Square root of 6
      • Square root of 49
      • Square root of 1
      • Square root of 32
      • Square root of 40
      • Square root of 81
      • Square root of 18
      • Square root of 72
      • Square root of 13
      • Square root of 80
      • Square root of 45
    • Log Calculator
    • Inequality Symbols
    • Exponent calculator
    • Decimal to Fraction Calculator
    • Fraction to Percent Calculator
    • Scale Factor
  • Unit Conversion
    • Celsius to Fahrenheit Converter >
      • 37 C to F
    • Fahrenheit to Celsius Converter >
      • 68 F to C
    • Kilograms to Pounds Converter >
      • 60 kg to lb
      • 80 kg to lbs
      • 150 kg to lbs
      • 100 kg to lbs
      • 50 kg to lbs
    • Pounds to Kilograms Converter >
      • 1 lb to kg
      • 10 lb to kg
      • 40 lb to kg
      • 50 lb to kg
      • 60 lb to kg
      • 90 lb to kg
      • 100 lb to kg
      • 130 lb to kg
      • 150 lb to kg
    • Fluid Ounces to Milliliters
    • Kilometers to Miles Converter >
      • 1 kilometer to miles
      • 5 km to miles
      • 10 km to miles
      • 15 km to miles
      • 20 km to miles
      • 50 km to miles
      • 100 km to miles
    • Miles to Kilometers Conversion >
      • 1 mile to kilometers
      • 5 miles to km
      • 10 miles to km
      • 15 miles to km
      • 20 miles to km
    • KPH to MPH Converter >
      • 300 kph to mph
    • Millimeters to Inches Converter
    • Meters to Feet Converter >
      • 1 Meter to Feet
      • 2 Meters to Feet
      • 3 Meters to Feet
      • 5 Meters to Feet
      • 10 Meters to Feet
      • 20 Meters to Feet
      • 30 Meters to Feet
      • 50 Meters to Feet
      • 100 Meters to Feet
    • Centimeters to Inches Converter >
      • 2 cm to inches
      • 3 cm to inches
      • 5 cm to inches
      • 8 cm to inches
      • 10 cm to inches
      • 12 cm to inches
      • 14 cm to inches
      • 15 cm to inches
      • 17 cm to inches
      • 18 cm to inches
      • 20 cm to inches
      • 21 cm to inches
      • 25 cm to inches
      • 28 cm to inches
      • 30 cm to inches
      • 35 cm to inches
      • 40 cm to inches
      • 50 cm to inches
      • 60 cm to inches
      • 36 cm to inches
      • 45 cm to inches
      • 70 cm to inches
      • 80 cm to inches
      • 90 cm to inches
      • 100 cm to inches
      • 120 cm to inches
      • 150 cm to inches
  • Date & Time
    • Time Conversion Chart
    • Military Times Chart
    • Time Zone
  • Test Prep
    • SAT Practice Test Math
    • Math Practice Test HiSET
    • Acing the SAT: A Comprehensive and Actionable Study Guide
    • GMAT Practice Questions Math with Answers and Explanations
    • GMAT Math Formulas Sheet
    • Math Practice Test for GED with Answers and Explanations
    • Math Problems to Solve | Practice Test
    • Free Practice TEAS Test
    • CFA Sample Practice Questions | Level 3| Answers and Explanations
    • CFA Level 2 Practice Exam Questions
    • How to Prepare for CFA level 1: An Actionable Study Guide
    • ​GRE Practice Math Questions | Free | Answers & Explanations
    • Formulas for GRE Math Section
    • ACT Practice Test with Answers and Explanations
    • CFA Practice Questions for level 1
    • CPA Practice Questions
    • ASVAB Practice Test
    • IQ Test
    • How many hours to study for CPA
    • How to Excel in Your CPA Exams: A Comprehensive Preparation Guide
  • Blog
  • Contact Us
    • Advertise Here
    • Privacy Policy
    • Useful Calculators and Converters
  • Español
    • XVIII Roman Numerals
    • XIX Roman Numerals
    • XX Roman Numerals
    • XXI Roman Numerals
    • XVIII Roman Numerals
    • XXII Roman Numerals
    • XXIII Roman Numerals
    • XXIV Roman Numerals
    • XXV Roman Numerals
    • XXVI Roman Numerals
    • XXVII Roman Numerals
    • XXVIII Roman Numerals
    • XXIX Roman Numerals
    • XXX Roman Numerals
    • XXXI Roman Numerals
    • XXXII Roman Numerals
    • XXXIII Roman Numerals
    • XXXIV Roman Numerals
    • XXXV Roman Numerals
    • XXXVI Roman Numerals
    • XXXVII Roman Numerals
    • XXXVIII Roman Numerals
    • XXXIX Roman Numerals
    • XL Roman Numerals
    • XLI Roman Numerals
  • Normal CDF Calculator
  • XVIII Roman Numerals

Radius of a Circle Calculator

​The Radius of a Circle Calculator is a helpful tool for anyone who needs to find the radius of a circle quickly and accurately. This calculator allows you to input the circle's diameter, circumference, or area, and it will instantly calculate the circle's radius for you. No more manual calculations or guesswork required! Whether you're a student, a professional, or simply someone who needs to find the radius of a circle, this calculator can help you save time and avoid errors. With its user-friendly interface and simple operation, you can easily input the necessary measurement and receive the result within seconds. So, whether you're working on a math problem or designing a circular object, the Radius of a Circle Calculator can assist you in finding the radius of a circle with ease.
Radius of a Circle Calculator

Radius of a Circle Calculator

Enter circumference, area or diameter to calculate the result:

Circumference (c):
Area (A):
Diameter (d):
Radius of the circle (r)

​The Radius of a Circle: Definition, Properties, and Applications

​In geometry, the radius of a circle holds great importance as one of its fundamental measurements. It is characterized as the distance between the center of the circle and any point on its perimeter. The radius plays a pivotal role in computing other attributes of a circle, including its diameter, circumference, and area. This article delves into the concept of the circle's radius, providing a comprehensive analysis of its definition, characteristics, and diverse applications.

Definition of the Radius of a Circle

​The radius of a circle can be defined as the measurement of the distance between its center and any point situated on its circumference. It is represented by the symbol ‘r’ and is usually measured in units of length, such as centimeters, meters, or inches. The radius is one of the two fundamental measurements used to describe the size of a circle, with the other being the diameter.

Properties of the Radius of a Circle

The radius of a circle has several important properties that are worth exploring. Some of these properties include:
 
  1. It can be stated that the radius of a circle is invariably equal to half of its diameter. This means that if the diameter of a circle is 10 units, then its radius will be 5 units.
  2. At any point on the circumference of a circle, the radius is consistently perpendicular to the tangent line. This is because the tangent line represents the direction in which the circle is changing most rapidly, and the radius always points directly towards the center of the circle.
  3. The length of the radius is proportional to the size of the circle. This means that as the size of a circle increases, so does its radius.
  4. The radius of a circle can be used to calculate its area and circumference. These calculations involve simple mathematical formulas that use the radius as a key input variable.

Applications of the Radius of a Circle

The radius of a circle is a fundamental measurement used in various fields, including mathematics, physics, and engineering. Some common applications of the radius of a circle include:
 
Calculating the area of a circle: The area of a circle is calculated using the formula A = πr^2, where ‘π’ is the mathematical constant pi (approximately equal to 3.14). By knowing the radius of a circle, it is possible to calculate its area, which is useful in various applications, such as calculating the area of a circular garden or a circular swimming pool.
 
Calculating the circumference of a circle: The circumference of a circle is calculated using the formula C = 2πr. By knowing the radius of a circle, it is possible to calculate its circumference, which is useful in various applications, such as measuring the length of a circular track or the distance around a circular object.
 
To determine the volume of a sphere, which is a three-dimensional object created by revolving a circle around its diameter, the formula V = (4/3)πr^3 can be used, where 'π' represents the mathematical constant pi. By having knowledge of the radius of the circle, it is feasible to compute the volume of the sphere produced by revolving it around its diameter.
 
Calculating the velocity of a rotating object: In physics, the velocity of a rotating object can be calculated using the formula v = ωr, where ‘v’ is the velocity of the object, ‘ω’ is the angular velocity (in radians per second), and ‘r’ is the radius of the circle that the object is rotating about. This formula is useful in various applications, such as calculating the speed of a spinning top or the velocity of a rotating turbine.
Radius of a circle

Examples of the Radius of a Circle

To better understand the concept of the radius of a circle, let us consider some examples:
 
A circular pizza has a diameter of 24 inches. What is the radius of the pizza?
 
Solution: The diameter of the pizza is given as 24 inches. Since the radius is always half of the diameter, we can calculate the radius by dividing the diameter by 2:
 
Radius = Diameter/2 = 24/2 = 12 inches
 
Therefore, the radius of the pizza is 12 inches.
 
The radius of a circular swimming pool is 5 meters. What is the circumference of the pool?
 
Solution: The radius of the pool is given as 5 meters. We can use the formula for the circumference of a circle to calculate the circumference of the pool:
 
Circumference = 2πr = 2 x 3.14 x 5 = 31.4 meters
 
Therefore, the circumference of the swimming pool is 31.4 meters.
 
A sphere has a radius of 3 centimeters. What is the volume of the sphere?
 
Solution: Given that the sphere has a radius of 3 centimeters, we can apply the formula for the volume of a sphere to determine its volume.
 
Volume = (4/3)πr^3 = (4/3) x 3.14 x 3^3 = 113.1 cubic centimeters
 
Therefore, the volume of the sphere is 113.1 cubic centimeters.
In conclusion, the radius of a circle is a fundamental measurement used in geometry and various other fields. It is defined as the distance from the center of a circle to any point on its circumference and has several important properties, such as being perpendicular to the tangent line at any point on the circumference and being proportional to the size of the circle. The radius is also used in various applications, such as calculating the area and circumference of a circle, the volume of a sphere, and the velocity of a rotating object.
Visit us at z-table.com for more math and stats calculators.
Proudly powered by Weebly
  • Z Table
    • Z Scores to Percentiles Chart
    • Z Score Calculator
    • Z Score Probability Calculator
    • Interactive Z Table
    • Z Score Formula
    • How to calculate the z score
    • How To Use Z-Score Table
    • Calculate Z-score
    • Parameters in Statistics
    • Z Score Chart Basics
    • History of Normal Distirbution
    • Statistics Z Score Jokes
    • When to Use Z Test vs T Test
    • Z Score Practice Problems
    • Confidence Interval Calculator >
      • Confidence Interval in Excel
      • 90 confidence interval z score
      • 95 Confidence Interval Z Score
      • 99 Confidence Interval Z Score
    • Z Score Confidence Interval
  • Statistics
    • Statistics Symbols
    • Statistics Formulas >
      • Binomial Coefficient
      • Empirical Rule
      • Correlation Coefficient
    • P Value Calculator >
      • P Value Calculator from Z Score
      • P Value Calculator from T Score
      • P Value Calculator from Chi-Square
      • P Value Calculator from F Ratio (ANOVA)
      • P Value Calculator from Pearson R
      • P Value Calculator Tukey's Q Score
    • Cumulative Binomial Probability Calculator
    • Interquartile Range Calculator
    • Empirical Rule Calculator
    • Mean, Median and Mode Calculator
    • Sample Size Calculator
    • Other Statistical Tables >
      • T Value Table
      • Chi-Square Table
      • F Distribution Table
    • Standard Deviation Calculator
    • Normal vs Non-Normal Distribution: Understanding the Differences
    • Explanatory Variable: Understanding Its Role in Statistical Analysis
    • Independent variable vs dependent
    • Statistics Forum
  • Math
    • Combination Calculator
    • Permutation Calculator
    • Exploring 7 Unsolvable Math Problems >
      • Riemann Hypothesis
    • Math Problems >
      • Math Problems for 1st Graders
      • Math Problems for 2nd Graders
      • Math Problems for 3rd Graders
      • Math Problems for 4th Graders
      • Math Problems for 5th Graders
      • Math Problems for 6th Graders
      • Math Problems for 7th Graders
      • Math Problems for 8th Graders
      • Math Problems for 9th Graders
      • Math Problems for 10th Graders
      • Math Problems for 11th Graders
    • Times Tables >
      • 1 Times Table
      • 2 Times Table
      • 3 Times Table
      • 4 Times Table
      • 5 Times Table
      • 6 Times Table
      • 7 Times Table
      • 8 Times Table
      • 9 Times Table
      • 10 Times Table
    • Multiplication Tables >
      • Multiplication Table by 20
      • Multiplication Table by 19
      • Multiplication Table by 18
      • Multiplication Table by 17
      • Multiplication Table by 16
      • Multiplication Table by 15
      • Multiplication Table by 14
      • Multiplication Table by 13
      • Multiplication Table by 12
      • Multiplication Table by 11
      • Multiplication Table by 10
      • Multiplication Table by 9
      • Multiplication Table by 8
      • Multiplication Table by 7
      • Multiplication Table by 6
      • Multiplication Table by 5
      • Multiplication Table by 4
      • Multiplication Table by 3
    • Roman Numerals >
      • Roman Numerals Chart
      • Roman Numerals Converter
      • I Roman Numerals
      • II Roman Numerals
      • III Roman Numerals
      • IV Roman Numerals
      • V Roman Numerals
      • VI Roman Numerals
      • VII Roman Numerals
      • VIII Roman Numerals
      • IX Roman Numerals
      • X Roman Numerals
      • XI Roman Numerals
      • XII Roman Numerals
      • XIII Roman Numerals
      • XIV Roman Numerals
      • XV Roman Numerals
      • XVI Roman Numerals
      • XVII Roman Numerals
      • XLVI Roman Numerals >
        • TEMP XVII Roman Numerals
    • Percentage Increase Calculator
    • Linear Equations >
      • Two-Variable Linear Equations Test with Answers
      • One Variable Linear Equations >
        • Ax=B Linear Equation Calculator
        • Ax=B Linear Equation Practice Test
    • Decimal Places Value Chart
    • Cone Volume Calculator
    • Rounding Calculator >
      • Round 15 to the nearest ten
      • Round 75 to the nearest ten
      • Round 35 to the nearest ten
      • Round 5 to the nearest ten
      • Round 3 to the Nearest Ten
    • Factor Calculator >
      • Factor of 36
      • Factor of 30
      • Factor of 32
      • Factor of 35
      • Factor of 39
      • Factor of 33
      • Factor of 34
      • Factor of 3
      • Factor of 3/4
      • Factor of 38
    • Radius of a Circle
    • Fraction Calculator
    • Random Number Generator
    • Horizontal Line
    • X and Y Axis
    • Root Calculator
    • Square Root Calculator >
      • Square root of 2
      • Square root of 8
      • Square root of 5
      • Square root of 4
      • Square root of 3
      • Square root of 64
      • Square root of 10
      • Square root of 16
      • Square root of 25
      • Square root of 12
      • Square root of 50
      • Square root of 20
      • Square root of 9
      • Square root of 100
      • Square root of 36
      • Square root of 6
      • Square root of 49
      • Square root of 1
      • Square root of 32
      • Square root of 40
      • Square root of 81
      • Square root of 18
      • Square root of 72
      • Square root of 13
      • Square root of 80
      • Square root of 45
    • Log Calculator
    • Inequality Symbols
    • Exponent calculator
    • Decimal to Fraction Calculator
    • Fraction to Percent Calculator
    • Scale Factor
  • Unit Conversion
    • Celsius to Fahrenheit Converter >
      • 37 C to F
    • Fahrenheit to Celsius Converter >
      • 68 F to C
    • Kilograms to Pounds Converter >
      • 60 kg to lb
      • 80 kg to lbs
      • 150 kg to lbs
      • 100 kg to lbs
      • 50 kg to lbs
    • Pounds to Kilograms Converter >
      • 1 lb to kg
      • 10 lb to kg
      • 40 lb to kg
      • 50 lb to kg
      • 60 lb to kg
      • 90 lb to kg
      • 100 lb to kg
      • 130 lb to kg
      • 150 lb to kg
    • Fluid Ounces to Milliliters
    • Kilometers to Miles Converter >
      • 1 kilometer to miles
      • 5 km to miles
      • 10 km to miles
      • 15 km to miles
      • 20 km to miles
      • 50 km to miles
      • 100 km to miles
    • Miles to Kilometers Conversion >
      • 1 mile to kilometers
      • 5 miles to km
      • 10 miles to km
      • 15 miles to km
      • 20 miles to km
    • KPH to MPH Converter >
      • 300 kph to mph
    • Millimeters to Inches Converter
    • Meters to Feet Converter >
      • 1 Meter to Feet
      • 2 Meters to Feet
      • 3 Meters to Feet
      • 5 Meters to Feet
      • 10 Meters to Feet
      • 20 Meters to Feet
      • 30 Meters to Feet
      • 50 Meters to Feet
      • 100 Meters to Feet
    • Centimeters to Inches Converter >
      • 2 cm to inches
      • 3 cm to inches
      • 5 cm to inches
      • 8 cm to inches
      • 10 cm to inches
      • 12 cm to inches
      • 14 cm to inches
      • 15 cm to inches
      • 17 cm to inches
      • 18 cm to inches
      • 20 cm to inches
      • 21 cm to inches
      • 25 cm to inches
      • 28 cm to inches
      • 30 cm to inches
      • 35 cm to inches
      • 40 cm to inches
      • 50 cm to inches
      • 60 cm to inches
      • 36 cm to inches
      • 45 cm to inches
      • 70 cm to inches
      • 80 cm to inches
      • 90 cm to inches
      • 100 cm to inches
      • 120 cm to inches
      • 150 cm to inches
  • Date & Time
    • Time Conversion Chart
    • Military Times Chart
    • Time Zone
  • Test Prep
    • SAT Practice Test Math
    • Math Practice Test HiSET
    • Acing the SAT: A Comprehensive and Actionable Study Guide
    • GMAT Practice Questions Math with Answers and Explanations
    • GMAT Math Formulas Sheet
    • Math Practice Test for GED with Answers and Explanations
    • Math Problems to Solve | Practice Test
    • Free Practice TEAS Test
    • CFA Sample Practice Questions | Level 3| Answers and Explanations
    • CFA Level 2 Practice Exam Questions
    • How to Prepare for CFA level 1: An Actionable Study Guide
    • ​GRE Practice Math Questions | Free | Answers & Explanations
    • Formulas for GRE Math Section
    • ACT Practice Test with Answers and Explanations
    • CFA Practice Questions for level 1
    • CPA Practice Questions
    • ASVAB Practice Test
    • IQ Test
    • How many hours to study for CPA
    • How to Excel in Your CPA Exams: A Comprehensive Preparation Guide
  • Blog
  • Contact Us
    • Advertise Here
    • Privacy Policy
    • Useful Calculators and Converters
  • Español
    • XVIII Roman Numerals
    • XIX Roman Numerals
    • XX Roman Numerals
    • XXI Roman Numerals
    • XVIII Roman Numerals
    • XXII Roman Numerals
    • XXIII Roman Numerals
    • XXIV Roman Numerals
    • XXV Roman Numerals
    • XXVI Roman Numerals
    • XXVII Roman Numerals
    • XXVIII Roman Numerals
    • XXIX Roman Numerals
    • XXX Roman Numerals
    • XXXI Roman Numerals
    • XXXII Roman Numerals
    • XXXIII Roman Numerals
    • XXXIV Roman Numerals
    • XXXV Roman Numerals
    • XXXVI Roman Numerals
    • XXXVII Roman Numerals
    • XXXVIII Roman Numerals
    • XXXIX Roman Numerals
    • XL Roman Numerals
    • XLI Roman Numerals
  • Normal CDF Calculator
  • XVIII Roman Numerals
x
x