🔢

Math & Utilities Calculators

Mathematical calculators, converters, and utility tools for everyday calculations

17 professional calculators available

Math Calculators for Percentages, Grades, Statistics & Homework

Fast, free math calculators for students, teachers, and everyday problem solving. Use our tools to calculate percentages, fractions, GPA, averages, ratios, probability, and classroom statistics with clear formulas and step-by-step explanations.

Top toolsStudent helpStatisticsEveryday math

From quick percentage change answers to grade goal planning, our math hub supports homework, exam prep, budgeting, and data analysis with tools built for real search intent.

Percentage Calculator

Percent of, increase, decrease, and difference

Fraction Calculator

Add, subtract, multiply, divide, simplify fractions

GPA Calculator

Semester, cumulative, weighted GPA on multiple scales

Average Calculator

Mean, median, mode, and dataset averages

🔥 Most Popular Math Calculations

Quick access to the most searched math problems:

Percentage Calculations

Percentage Increase/Decrease

GPA Calculations

Fraction Calculations

Grade Calculations

Statistics Calculations

Ratio Calculations

📊 Math Reference Tables & Formula Guide

Common Percentage Calculations

PercentageOf 100Of 200Of 500Of 1000
5%5102550
10%102050100
15%153075150
20%2040100200
25%2550125250
30%3060150300
40%4080200400
50%50100250500
75%75150375750
100%1002005001000
💡 Quick Tip: 10% = divide by 10, 50% = divide by 2, 25% = divide by 4
Calculate any percentage →

Percentage Formulas Reference

CalculationFormulaExample
X% of Y(X ÷ 100) × Y20% of 150 = (20÷100)×150 = 30
X is what % of Y(X ÷ Y) × 10030 is what % of 150? = (30÷150)×100 = 20%
% Increase((New - Old) ÷ Old) × 10050→75: (75-50)÷50×100 = 50%
% Decrease((Old - New) ÷ Old) × 100100→80: (100-80)÷100×100 = 20%
Increase X by Y%X × (1 + Y÷100)100 + 20% = 100×1.2 = 120
Decrease X by Y%X × (1 - Y÷100)100 - 20% = 100×0.8 = 80

GPA Scale Conversion (4.0 Scale)

Letter Grade to GPA:

LetterGrade %4.0 GPA5.0 GPA (Weighted)Description
A+97-1004.05.0Excellent
A93-964.05.0Excellent
A-90-923.74.5Very Good
B+87-893.34.0Good
B83-863.03.5Good
B-80-822.73.0Above Average
C+77-792.32.5Average
C73-762.02.0Average
C-70-721.71.5Below Average
D+67-691.31.0Poor
D65-661.01.0Poor
FBelow 650.00.0Failing
GPA Quality:
  • 4.0: Perfect, summa cum laude
  • 3.7-3.9: Excellent, magna cum laude
  • 3.5-3.69: Very good, cum laude
  • 3.0-3.49: Good, honors
  • 2.5-2.99: Average
  • 2.0-2.49: Below average
  • Below 2.0: Poor, academic probation
Calculate your GPA →

Common Fractions & Decimal Equivalents

FractionDecimalPercentageMemory Tip
1/20.550%Half
1/30.333...33.33%Third
2/30.666...66.67%Two-thirds
1/40.2525%Quarter
3/40.7575%Three-quarters
1/50.220%Fifth
2/50.440%Two-fifths
3/50.660%Three-fifths
4/50.880%Four-fifths
1/80.12512.5%Eighth
3/80.37537.5%Three-eighths
5/80.62562.5%Five-eighths
7/80.87587.5%Seven-eighths
1/100.110%Tenth
1/1000.011%Hundredth
Convert fractions →

Statistical Measures Quick Reference

When to Use Each:

MeasureBest ForExampleFormula
Mean (Average)Evenly distributed dataTest scores: 80, 85, 90 → Mean = 85Sum ÷ Count
MedianData with outliersSalaries: 40K, 45K, 50K, 500K → Median = 47.5KMiddle value
ModeMost common valueShoe sizes: 8, 9, 9, 10, 9 → Mode = 9Most frequent
RangeData spreadTemps: 20°, 25°, 30° → Range = 10°Max - Min
Standard DeviationVariability measureTest scores: how spread out?√(Σ(x-μ)²/n)
VarianceData dispersionInvestment risk analysisσ²
Example Dataset: [10, 12, 14, 16, 18]
  • Mean: 14
  • Median: 14
  • Mode: No mode (all unique)
  • Range: 8 (18-10)
  • Standard Deviation: 2.83

Ratio & Proportion Reference

Common Ratios:

RatioEquivalentPercentageCommon Use
1:150:5050%-50%Equal split
1:233:6733%-67%Recipe scaling
2:340:6040%-60%Aspect ratios
3:443:5743%-57%Old TV screen
4:544:5644%-56%Photo print
9:1636:6436%-64%Smartphone screen
16:964:3664%-36%Widescreen TV
21:970:3070%-30%Ultrawide monitor
Simplifying Ratios:
  1. Find GCD (Greatest Common Divisor)
  2. Divide both numbers by GCD
  3. Example: 12:18 → GCD=6 → 2:3
Calculate ratios →

Grade Calculation Scenarios

Weighted Grade Calculation:

CategoryWeightYour ScoreWeighted Score
Tests40%85%34%
Homework30%90%27%
Projects20%80%16%
Participation10%95%9.5%
Final Grade100%-86.5%
What Grade Do I Need?

Example: Current grade 80%, Final exam 25% weight, want 85% overall

  • Formula: (Target - Current×(1-Weight)) ÷ Weight
  • Calculation: (85 - 80×0.75) ÷ 0.25 = 100%
  • Need: 100% on final (perfect score!)
Calculate grade needs →

📚 Complete Math Calculation Guides

Step-by-step guides to master common math calculations, from percentages to statistics.

How to Calculate Percentages (Step-by-Step)

Method 1: What is X% of Y?

Formula: (X ÷ 100) × Y

Example 1: What is 20% of 150?

  1. Convert percentage to decimal: 20 ÷ 100 = 0.20
  2. Multiply by the number: 0.20 × 150 = 30
  3. Answer: 30

Example 2: What is 15% of 80?

  1. 15 ÷ 100 = 0.15
  2. 0.15 × 80 = 12
  3. Answer: 12

💡 Mental Math Shortcut:

  • 10%: Divide by 10 (10% of 200 = 20)
  • 20%: Calculate 10% then double (20% of 200 = 40)
  • 5%: Calculate 10% then halve (5% of 200 = 10)
  • 25%: Divide by 4 (25% of 200 = 50)
  • 50%: Divide by 2 (50% of 200 = 100)

Method 2: X is What % of Y?

Formula: (X ÷ Y) × 100

Example 1: 30 is what percent of 150?

  1. Divide X by Y: 30 ÷ 150 = 0.2
  2. Multiply by 100: 0.2 × 100 = 20
  3. Answer: 20%

Example 2: 45 is what percent of 180?

  1. 45 ÷ 180 = 0.25
  2. 0.25 × 100 = 25
  3. Answer: 25%

Method 3: Percentage Increase/Decrease

Increase Formula: ((New - Old) ÷ Old) × 100
Decrease Formula: ((Old - New) ÷ Old) × 100

Example - Price Increase:

Old price: ₹100, New price: ₹120

  1. Find difference: 120 - 100 = 20
  2. Divide by old: 20 ÷ 100 = 0.20
  3. Multiply by 100: 0.20 × 100 = 20%
  4. Answer: 20% increase

Example - Discount:

Original: ₹200, Sale: ₹160

  1. Difference: 200 - 160 = 40
  2. Divide: 40 ÷ 200 = 0.20
  3. Multiply: 0.20 × 100 = 20%
  4. Answer: 20% discount
Calculate percentages →

How to Calculate GPA (Complete Guide)

Step 1: Know Your Grading Scale

Standard 4.0 Scale:

  • A = 4.0
  • B = 3.0
  • C = 2.0
  • D = 1.0
  • F = 0.0

With Plus/Minus:

  • A+ = 4.0, A = 4.0, A- = 3.7
  • B+ = 3.3, B = 3.0, B- = 2.7
  • C+ = 2.3, C = 2.0, C- = 1.7
  • D+ = 1.3, D = 1.0, F = 0.0

Step 2: List Your Grades

Example semester:

SubjectGradeCreditsPoints
MathA312
EnglishB+39.9
HistoryA-311.1
ScienceB412
ElectiveA28

Step 3: Calculate GPA

  1. Total grade points: 12 + 9.9 + 11.1 + 12 + 8 = 53
  2. Total credits: 3 + 3 + 3 + 4 + 2 = 15
  3. GPA = 53 ÷ 15 = 3.53

Weighted GPA (Honors/AP Classes)

  • Regular: 4.0 scale
  • Honors: +0.5 (A = 4.5)
  • AP/IB: +1.0 (A = 5.0)

Example with AP:

  • AP Math: A = 5.0 × 3 = 15
  • Regular English: B+ = 3.3 × 3 = 9.9
  • Weighted GPA = (15 + 9.9) ÷ 6 = 4.15
Calculate GPA →

How to Calculate Fractions

Adding Fractions

Same Denominator:

1/4 + 2/4 = (1+2)/4 = 3/4

Different Denominators:

1/2 + 1/3

  1. Find LCD (Least Common Denominator) = 6
  2. Convert: 1/2 = 3/6, 1/3 = 2/6
  3. Add: 3/6 + 2/6 = 5/6

Subtracting Fractions

3/4 - 1/2

  1. LCD = 4
  2. Convert: 1/2 = 2/4
  3. Subtract: 3/4 - 2/4 = 1/4

Multiplying Fractions

2/3 × 3/4

  1. Multiply numerators: 2 × 3 = 6
  2. Multiply denominators: 3 × 4 = 12
  3. Simplify: 6/12 = 1/2

Dividing Fractions

1/2 ÷ 1/4

  1. Flip second fraction: 1/4 → 4/1
  2. Multiply: 1/2 × 4/1 = 4/2
  3. Simplify: 4/2 = 2
Calculate fractions →

Understanding Statistics (Mean, Median, Mode)

When to Use Each

MeasureBest ForExampleFormula
Mean (Average)Evenly distributed data, no outliersTest scores: 80, 85, 90, 95 → Mean = 87.5Sum ÷ Count
MedianData with outliers or skewed distributionSalaries: $30K, $35K, $40K, $500K → Median = $37.5KMiddle value
ModeFinding most frequent valueShirt sizes: S, M, M, L, M, XL → Mode = MMost frequent

Real-World Example

Home prices in neighborhood:

$200K, $220K, $230K, $240K, $2M (mansion)

  • Mean: $578K (misleading due to mansion)
  • Median: $230K (better representation)
  • Mode: No mode (all unique)

✅ Best choice: Median ($230K) represents typical home price

Calculate statistics →

How to Calculate Ratios and Proportions

Simplifying Ratios

Example: Simplify 12:18

  1. Find GCD (Greatest Common Divisor) of 12 and 18 = 6
  2. Divide both numbers by GCD: 12÷6 = 2, 18÷6 = 3
  3. Simplified ratio: 2:3

Finding Missing Values in Proportions

Example: Find X in 3:5 = X:15

Cross multiply: 3 × 15 = 5 × X

  1. 45 = 5X
  2. X = 45 ÷ 5 = 9
  3. Answer: X = 9

Real-World Applications

  • Recipe Scaling: If recipe serves 4 (2 cups flour), for 8 people: 2:4 = X:8 → X = 4 cups
  • Map Scale: 1 cm = 5 km, so 3 cm = ? → 1:5 = 3:X → X = 15 km
  • Mixing Solutions: Mix paint 2:3 (red:blue), for 10 parts total: 2:3 = 4:6
Calculate ratios →

How to Calculate Weighted Grades

Step-by-Step Process

Example: Calculate final grade with weighted categories

CategoryWeightYour ScoreWeighted Score
Tests40%85%34%
Homework30%90%27%
Projects20%80%16%
Participation10%95%9.5%
Final Grade100%-86.5%

Formula: Weighted Score = (Your Score × Weight) for each category, then sum all weighted scores

What Grade Do I Need on Final?

Example: Current grade 80%, Final exam 25% weight, want 85% overall

Formula: (Target - Current×(1-Weight)) ÷ Weight

  1. Current portion: 80% × (1 - 0.25) = 80% × 0.75 = 60%
  2. Need from final: 85% - 60% = 25%
  3. Final score needed: 25% ÷ 0.25 = 100%
  4. Answer: Need 100% on final (perfect score!)
Calculate grade needs →

Browse Math & Utilities Calculators

Start with the most popular math tool for homework and everyday calculations: percentage change, discounts, grade goals, averages, and fraction problems. This calculator is fast, accurate, and built for the questions students and professionals search for most.

Open Percentage Calculator →

Also explore: Fraction Calculator, GPA Calculator, and Average Calculator.

❓ Frequently Asked Questions About Math Calculations

Frequently Asked Questions