Math & Utilities Calculators
Mathematical calculators, converters, and utility tools for everyday calculations
Math Calculators: Essential Tools for Statistical Analysis and Mathematical Computations
Our math calculator suite provides comprehensive tools for statistical analysis, mathematical computations, and academic problem-solving. Whether you're calculating mean, median, variance, or standard deviation for datasets, converting between number formats, or performing basic mathematical operations, our calculators help you solve problems accurately and efficiently. Perfect for students, researchers, data analysts, and anyone working with numerical data.
Available Calculators: Our Average Calculator calculates the mean of any dataset instantly. The Median Calculator finds the middle value in sorted data, ideal for skewed distributions. Our Variance Calculator measures data spread and variability. The Case Converter transforms text between different case formats for programming and writing.
Statistical Tools: Calculate standard deviation, mode, range, and other statistical measures. All calculators use validated mathematical formulas, provide step-by-step explanations, and help you understand how calculations work. Whether you're analyzing test scores, research data, quality control metrics, or any numerical dataset, our calculators provide the accuracy and insights you need for mathematical analysis and decision-making.
π₯ 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
π Math Reference Tables & Formula Guide
Common Percentage Calculations
| Percentage | Of 100 | Of 200 | Of 500 | Of 1000 |
|---|---|---|---|---|
| 5% | 5 | 10 | 25 | 50 |
| 10% | 10 | 20 | 50 | 100 |
| 15% | 15 | 30 | 75 | 150 |
| 20% | 20 | 40 | 100 | 200 |
| 25% | 25 | 50 | 125 | 250 |
| 30% | 30 | 60 | 150 | 300 |
| 40% | 40 | 80 | 200 | 400 |
| 50% | 50 | 100 | 250 | 500 |
| 75% | 75 | 150 | 375 | 750 |
| 100% | 100 | 200 | 500 | 1000 |
Percentage Formulas Reference
| Calculation | Formula | Example |
|---|---|---|
| X% of Y | (X Γ· 100) Γ Y | 20% of 150 = (20Γ·100)Γ150 = 30 |
| X is what % of Y | (X Γ· Y) Γ 100 | 30 is what % of 150? = (30Γ·150)Γ100 = 20% |
| % Increase | ((New - Old) Γ· Old) Γ 100 | 50β75: (75-50)Γ·50Γ100 = 50% |
| % Decrease | ((Old - New) Γ· Old) Γ 100 | 100β80: (100-80)Γ·100Γ100 = 20% |
| Increase X by Y% | X Γ (1 + YΓ·100) | 100 + 20% = 100Γ1.2 = 120 |
| Decrease X by Y% | X Γ (1 - YΓ·100) | 100 - 20% = 100Γ0.8 = 80 |
GPA Scale Conversion (4.0 Scale)
Letter Grade to GPA:
| Letter | Grade % | 4.0 GPA | 5.0 GPA (Weighted) | Description |
|---|---|---|---|---|
| A+ | 97-100 | 4.0 | 5.0 | Excellent |
| A | 93-96 | 4.0 | 5.0 | Excellent |
| A- | 90-92 | 3.7 | 4.5 | Very Good |
| B+ | 87-89 | 3.3 | 4.0 | Good |
| B | 83-86 | 3.0 | 3.5 | Good |
| B- | 80-82 | 2.7 | 3.0 | Above Average |
| C+ | 77-79 | 2.3 | 2.5 | Average |
| C | 73-76 | 2.0 | 2.0 | Average |
| C- | 70-72 | 1.7 | 1.5 | Below Average |
| D+ | 67-69 | 1.3 | 1.0 | Poor |
| D | 65-66 | 1.0 | 1.0 | Poor |
| F | Below 65 | 0.0 | 0.0 | Failing |
- 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
Common Fractions & Decimal Equivalents
| Fraction | Decimal | Percentage | Memory Tip |
|---|---|---|---|
| 1/2 | 0.5 | 50% | Half |
| 1/3 | 0.333... | 33.33% | Third |
| 2/3 | 0.666... | 66.67% | Two-thirds |
| 1/4 | 0.25 | 25% | Quarter |
| 3/4 | 0.75 | 75% | Three-quarters |
| 1/5 | 0.2 | 20% | Fifth |
| 2/5 | 0.4 | 40% | Two-fifths |
| 3/5 | 0.6 | 60% | Three-fifths |
| 4/5 | 0.8 | 80% | Four-fifths |
| 1/8 | 0.125 | 12.5% | Eighth |
| 3/8 | 0.375 | 37.5% | Three-eighths |
| 5/8 | 0.625 | 62.5% | Five-eighths |
| 7/8 | 0.875 | 87.5% | Seven-eighths |
| 1/10 | 0.1 | 10% | Tenth |
| 1/100 | 0.01 | 1% | Hundredth |
Statistical Measures Quick Reference
When to Use Each:
| Measure | Best For | Example | Formula |
|---|---|---|---|
| Mean (Average) | Evenly distributed data | Test scores: 80, 85, 90 β Mean = 85 | Sum Γ· Count |
| Median | Data with outliers | Salaries: 40K, 45K, 50K, 500K β Median = 47.5K | Middle value |
| Mode | Most common value | Shoe sizes: 8, 9, 9, 10, 9 β Mode = 9 | Most frequent |
| Range | Data spread | Temps: 20Β°, 25Β°, 30Β° β Range = 10Β° | Max - Min |
| Standard Deviation | Variability measure | Test scores: how spread out? | β(Ξ£(x-ΞΌ)Β²/n) |
| Variance | Data dispersion | Investment risk analysis | ΟΒ² |
- Mean: 14
- Median: 14
- Mode: No mode (all unique)
- Range: 8 (18-10)
- Standard Deviation: 2.83
Ratio & Proportion Reference
Common Ratios:
| Ratio | Equivalent | Percentage | Common Use |
|---|---|---|---|
| 1:1 | 50:50 | 50%-50% | Equal split |
| 1:2 | 33:67 | 33%-67% | Recipe scaling |
| 2:3 | 40:60 | 40%-60% | Aspect ratios |
| 3:4 | 43:57 | 43%-57% | Old TV screen |
| 4:5 | 44:56 | 44%-56% | Photo print |
| 9:16 | 36:64 | 36%-64% | Smartphone screen |
| 16:9 | 64:36 | 64%-36% | Widescreen TV |
| 21:9 | 70:30 | 70%-30% | Ultrawide monitor |
- Find GCD (Greatest Common Divisor)
- Divide both numbers by GCD
- Example: 12:18 β GCD=6 β 2:3
Grade Calculation Scenarios
Weighted Grade Calculation:
| Category | Weight | Your Score | Weighted Score |
|---|---|---|---|
| Tests | 40% | 85% | 34% |
| Homework | 30% | 90% | 27% |
| Projects | 20% | 80% | 16% |
| Participation | 10% | 95% | 9.5% |
| Final Grade | 100% | - | 86.5% |
Example: Current grade 80%, Final exam 25% weight, want 85% overall
- Formula: (Target - CurrentΓ(1-Weight)) Γ· Weight
- Calculation: (85 - 80Γ0.75) Γ· 0.25 = 100%
- Need: 100% on final (perfect score!)
π 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 Γ· 100) Γ Y
Example 1: What is 20% of 150?
- Convert percentage to decimal: 20 Γ· 100 = 0.20
- Multiply by the number: 0.20 Γ 150 = 30
- Answer: 30
Example 2: What is 15% of 80?
- 15 Γ· 100 = 0.15
- 0.15 Γ 80 = 12
- Answer: 12
π‘ 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 Γ· Y) Γ 100
Example 1: 30 is what percent of 150?
- Divide X by Y: 30 Γ· 150 = 0.2
- Multiply by 100: 0.2 Γ 100 = 20
- Answer: 20%
Example 2: 45 is what percent of 180?
- 45 Γ· 180 = 0.25
- 0.25 Γ 100 = 25
- Answer: 25%
Method 3: Percentage Increase/Decrease
Increase Formula: ((New - Old) Γ· Old) Γ 100
Decrease Formula: ((Old - New) Γ· Old) Γ 100
Example - Price Increase:
Old price: βΉ100, New price: βΉ120
- Find difference: 120 - 100 = 20
- Divide by old: 20 Γ· 100 = 0.20
- Multiply by 100: 0.20 Γ 100 = 20%
- Answer: 20% increase
Example - Discount:
Original: βΉ200, Sale: βΉ160
- Difference: 200 - 160 = 40
- Divide: 40 Γ· 200 = 0.20
- Multiply: 0.20 Γ 100 = 20%
- Answer: 20% discount
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:
| Subject | Grade | Credits | Points |
|---|---|---|---|
| Math | A | 3 | 12 |
| English | B+ | 3 | 9.9 |
| History | A- | 3 | 11.1 |
| Science | B | 4 | 12 |
| Elective | A | 2 | 8 |
Step 3: Calculate GPA
- Total grade points: 12 + 9.9 + 11.1 + 12 + 8 = 53
- Total credits: 3 + 3 + 3 + 4 + 2 = 15
- GPA = 53 Γ· 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 Γ 3 = 15
- Regular English: B+ = 3.3 Γ 3 = 9.9
- Weighted GPA = (15 + 9.9) Γ· 6 = 4.15
How to Calculate Fractions
Adding Fractions
Same Denominator:
1/4 + 2/4 = (1+2)/4 = 3/4
Different Denominators:
1/2 + 1/3
- Find LCD (Least Common Denominator) = 6
- Convert: 1/2 = 3/6, 1/3 = 2/6
- Add: 3/6 + 2/6 = 5/6
Subtracting Fractions
3/4 - 1/2
- LCD = 4
- Convert: 1/2 = 2/4
- Subtract: 3/4 - 2/4 = 1/4
Multiplying Fractions
2/3 Γ 3/4
- Multiply numerators: 2 Γ 3 = 6
- Multiply denominators: 3 Γ 4 = 12
- Simplify: 6/12 = 1/2
Dividing Fractions
1/2 Γ· 1/4
- Flip second fraction: 1/4 β 4/1
- Multiply: 1/2 Γ 4/1 = 4/2
- Simplify: 4/2 = 2
Understanding Statistics (Mean, Median, Mode)
When to Use Each
| Measure | Best For | Example | Formula |
|---|---|---|---|
| Mean (Average) | Evenly distributed data, no outliers | Test scores: 80, 85, 90, 95 β Mean = 87.5 | Sum Γ· Count |
| Median | Data with outliers or skewed distribution | Salaries: $30K, $35K, $40K, $500K β Median = $37.5K | Middle value |
| Mode | Finding most frequent value | Shirt sizes: S, M, M, L, M, XL β Mode = M | Most 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)
β Best choice: Median ($230K) represents typical home price
How to Calculate Ratios and Proportions
Simplifying Ratios
Example: Simplify 12:18
- Find GCD (Greatest Common Divisor) of 12 and 18 = 6
- Divide both numbers by GCD: 12Γ·6 = 2, 18Γ·6 = 3
- Simplified ratio: 2:3
Finding Missing Values in Proportions
Example: Find X in 3:5 = X:15
Cross multiply: 3 Γ 15 = 5 Γ X
- 45 = 5X
- X = 45 Γ· 5 = 9
- Answer: X = 9
Real-World Applications
- Recipe Scaling: If recipe serves 4 (2 cups flour), for 8 people: 2:4 = X:8 β X = 4 cups
- Map Scale: 1 cm = 5 km, so 3 cm = ? β 1:5 = 3:X β X = 15 km
- Mixing Solutions: Mix paint 2:3 (red:blue), for 10 parts total: 2:3 = 4:6
How to Calculate Weighted Grades
Step-by-Step Process
Example: Calculate final grade with weighted categories
| Category | Weight | Your Score | Weighted Score |
|---|---|---|---|
| Tests | 40% | 85% | 34% |
| Homework | 30% | 90% | 27% |
| Projects | 20% | 80% | 16% |
| Participation | 10% | 95% | 9.5% |
| Final Grade | 100% | - | 86.5% |
Formula: Weighted Score = (Your Score Γ 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 - CurrentΓ(1-Weight)) Γ· Weight
- Current portion: 80% Γ (1 - 0.25) = 80% Γ 0.75 = 60%
- Need from final: 85% - 60% = 25%
- Final score needed: 25% Γ· 0.25 = 100%
- Answer: Need 100% on final (perfect score!)
Percentage Calculator
Free percentage calculator for all calculations: what is X% of Y, percentage increase, percentage decrease, percentage difference, apply percentage change. Includes formulas, real-world examples for shopping discounts, tips, salary raises, grades, and comprehensive percentage math guide.
GPA Calculator
Calculate GPA (Grade Point Average) for high school or college students. Convert letter grades to GPA on 4.0 scale with weighted classes, honors, and AP courses.
Average Calculator
Calculate mean average of any set of numbers. Find arithmetic mean, sum, and count for statistics, grades, scores, or data analysis with weighted average option.
Final Grade Calculator
Calculate final grades with weighted categories (tests, homework, projects). Determine what grade you need on final exam and track current class grade with percentage breakdowns.
Case Converter Tool
Convert text between 14+ case formats instantly - uppercase, lowercase, title case, camelCase, snake_case, kebab-case, and more. Transform text formatting for coding and writing.
Percentage Increase Calculator
Calculate percentage increase between two numbers. Find percent growth, price increase, salary raise, and relative change with step-by-step percentage increase formula.
Fraction Calculator
Add, subtract, multiply, and divide fractions. Simplify fractions, convert mixed numbers, find common denominators, and solve fraction math problems step-by-step.
Percentage Decrease Calculator
Calculate percentage decrease between two numbers. Find percent reduction, discount amount, loss percentage, and decline rate with percentage decrease formula.
Ratio Calculator
Calculate and simplify ratios, find equivalent ratios, and solve ratio problems. Convert ratios to fractions, percentages, and proportions for math and real-world applications.
Standard Deviation Calculator
Calculate standard deviation, variance, mean, and range for sample or population data. Measure data dispersion and variability with step-by-step statistical calculations.
Decimal Calculator
Convert between decimals and fractions. Add, subtract, multiply, divide decimals with precise calculations and step-by-step decimal to fraction conversion.
Median Calculator
Calculate median (middle value) of a dataset. Find median for even/odd number sets, sorted data, and statistical analysis with step-by-step median calculation.
Variance Calculator
Calculate variance of sample or population dataset. Measure data spread, deviation from mean, and statistical variability with population and sample variance formulas.
Random Word Generator
Generate unique random words with history tracking! English & Hindi word generator with no duplicates. Track all generated words, copy history, and get fresh vocabulary every time. Perfect for creative writing, brainstorming, and games.
Mode Calculator
Calculate mode (most frequent value) in a dataset. Find modal value, frequency distribution, and multiple modes for statistical analysis and data interpretation.
CGPA to GPA Converter
Free CGPA to GPA converter for Indian students applying to US/UK universities. Convert your 10-point CGPA to 4.0 GPA scale instantly. Includes university-specific conversions (MIT, Stanford, UT Austin), percentage equivalent, and grade interpretation.
SGPA to CGPA Calculator
Free SGPA to CGPA calculator for Indian students. Calculate your cumulative CGPA from semester GPAs instantly. Supports 10-point scale, shows grade interpretation, percentage equivalent, and semester-by-semester breakdown.