Sector Angle in Pie Chart with Formula and Examples

Sector Angle in Pie Chart represents the central angle occupied by a category. Since a complete pie chart measures 360°, the angle for any category is proportional to its value. This page explains the sector angle formula, finding values from angles, percentage conversions, ratio-based methods and solved aptitude examples.

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What Is a Sector Angle in a Pie Chart?

The sector angle in a pie chart is the angle at the centre formed by the two radii marking a category. It is calculated as the category value divided by the total value, multiplied by 360°.

If a category has value x and the total of all categories is T, then its sector angle is θ = (x/T) × 360°. The sum of all sector angles in a complete pie chart is 360°. For example, if a category represents 25% of the total, its sector angle is 25/100 × 360° = 90°.

Sector Angle in Pie Chart Video Lessons

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Pie Chart Reverse Problems and Angles

Learn to solve reverse problems in pie charts and calculate sector angles from given data, proportions, or percentages using clear quantitative aptitude methods.

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Sector Angle in Pie Chart Formula & Tricks

Important Formulas

Sector angle from category value
θ = (x ÷ T) × 360°

Here, x is the value of the category, T is the total value of all categories and θ is the sector angle.

Category value from sector angle
x = (θ ÷ 360°) × T

Use this formula when the sector angle and the total value are given.

Percentage from sector angle
Percentage = (θ ÷ 360°) × 100 = θ ÷ 3.6

A sector angle can be converted directly into a percentage of the total.

Angle from percentage
θ = Percentage × 3.6°

Each 1% of a pie chart corresponds to 3.6° because 360° ÷ 100 = 3.6°.

Quick Tricks

Use standard percentage angles

Remember that 10% = 36°, 25% = 90°, 50% = 180° and 75% = 270°. These values reduce calculation time.

Example: A category occupying 25% of a pie chart has sector angle 90°.
Use ratios directly

Sector angles are proportional to category values. If two values are in the ratio a:b, their sector angles are also in the ratio a:b.

Example: Values 30 and 20 have angles in the ratio 3:2. If their combined angle is 180°, the angles are 108° and 72°.
Find the missing angle by subtraction

The complete pie chart is 360°. Subtract the known sector angles from 360° to find the remaining sector angle.

Example: If three sectors measure 80°, 110° and 95°, the fourth sector is 360° − 285° = 75°.

Sector Angle in Pie Chart Concepts

Calculating the Angle from a Given Value

Divide the category value by the total value and multiply the result by 360°.

For a category value x among total T, use θ = (x/T) × 360°. First find the total of all categories, then simplify the fraction before multiplying by 360° where possible.

Example: For values 20, 30, 25 and 25, the total is 100. The angle for value 30 is (30/100) × 360° = 108°.

Finding a Category Value from Its Angle

Multiply the sector angle by the total value and divide by 360°.

When θ and T are known, use x = (θ/360°) × T. The resulting value has the same unit as the total, such as persons, rupees, tonnes or units.

Example: If a sector measures 72° and the total number of students is 500, its value is (72/360) × 500 = 100 students.

Converting Sector Angles into Percentages

A sector angle represents θ/360 of the whole, so its percentage is θ/3.6.

The percentage corresponding to an angle is calculated by (θ/360) × 100. Thus, 90° represents 25%, while 144° represents 40%.

Example: For a 126° sector, the percentage is 126/3.6 = 35%.

Comparing Sectors and Finding Missing Angles

The ratio of sector angles equals the ratio of their category values, and all sector angles together equal 360°.

For two categories, x₁:x₂ = θ₁:θ₂. If some angles are known, subtract their sum from 360° to obtain the missing angle. This missing angle can then be converted into a value using x = (θ/360°) × T.

Example: If sectors for A, B and C are 90°, 120° and 60°, the remaining sector is 90°. Its share is 90/360 = 25%.

Sector Angle in Pie Chart Visual Guide & Data

Use the table and chart below to understand the data better.

Source Data for Sector-Angle Calculation

Category values and their corresponding sector angles in a pie chart.

Category Number of students Sector angle
Mathematics 20 72°
English 30 108°
Science 25 90°
Reasoning 25 90°

Note: Total students = 100 and total sector angle = 360°. Each angle is calculated as (category value ÷ 100) × 360°.

Subject-wise Distribution of Students

Visual guide: Subject-wise Distribution of Students
The pie chart uses the source-table values; each sector angle is proportional to the number of students.

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Practice Sector Angle in Pie Chart Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Sector Angle in Pie Chart: Revision Points

Use these formulas and rules to solve sector-angle questions quickly and accurately.

  • A complete pie chart represents 360°.
  • Sector angle = (Category value ÷ Total value) × 360°.
  • Category value = (Sector angle ÷ 360°) × Total value.
  • Percentage = Sector angle ÷ 3.6.
  • The ratio of sector angles equals the ratio of category values.
  • The sum of all sector angles must be 360°.
  • A sector angle is measured at the centre of the pie chart.

Related Topic Explainers

Bar Graph Data Interpretation → Double Bar Graph → Stacked Bar Graph → Line Graph Data Interpretation → Growth Rate in Line Graph → Tabular Data Interpretation → Percentage Share in Table DI → Percentage Change in Table DI →

Sector Angle in Pie Chart FAQs

What is the sector angle in a pie chart for a value of 40 out of a total of 200?

Sector angle = (40/200) × 360° = 72°.

What value does a 54° sector represent if the total is 800?

Value = (54/360) × 800 = 120.

What percentage does a 108° sector represent?

Percentage = 108/3.6 = 30%.

How do you find a missing sector angle in a pie chart?

Subtract the sum of the known sector angles from 360°. For example, if the known angles total 245°, the missing angle is 115°.

What is the angle for 15% of a pie chart?

Angle = 15 × 3.6° = 54°.

If two categories have values in the ratio 4:5, what is the ratio of their sector angles?

Their sector-angle ratio is also 4:5 because sector angles are directly proportional to category values.

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