Complete Formula Reference Guide

Master mathematics with our comprehensive collection of 25+ calculator formulas. From automotive calculations to financial planning, health assessments to ratio analysis - all formulas include industry standards, accuracy metrics, and real-world examples.

Automotive Calculation Formulas

Professional automotive formulas for fuel economy, financing, gear ratios, and vehicle performance.

Car Loan Payment

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M = P × [r(1+r)ⁿ] / [(1+r)ⁿ - 1]
Variables: M = Monthly payment, P = Principal amount, r = Monthly interest rate, n = Number of payments

Description: Calculates monthly payments for auto loans with fixed interest rates.

Standard: Automotive Finance Industry Standard

Accuracy: Exact calculation (no rounding errors)

Common Use Cases:
  • Auto loan planning
  • Vehicle financing
  • Budget planning
Example:

$25,000 car loan, 5% APR, 60 months: Monthly payment = $471.78

Fuel Economy (MPG/L per 100km)

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MPG = Miles Driven / Gallons Used
Imperial: MPG = Total Miles / Total Gallons
Metric: L/100km = (Liters Used / Kilometers Driven) × 100

Description: Measures vehicle fuel efficiency in miles per gallon or liters per 100 kilometers.

Standard: EPA (Environmental Protection Agency) Standards

Accuracy: ±2-3% with accurate measurements

Common Use Cases:
  • Fuel cost planning
  • Vehicle comparison
  • Environmental impact
Example:

300 miles driven, 12 gallons used: MPG = 300/12 = 25 MPG

Gear Ratio Calculation

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Gear Ratio = Number of Teeth on Driving Gear / Number of Teeth on Driven Gear
Speed: Output Speed = Input Speed / Gear Ratio
Alternative: Gear Ratio = Input RPM / Output RPM

Description: Calculates mechanical advantage and speed reduction/increase in gear systems.

Standard: Mechanical Engineering Standards

Accuracy: Mathematically exact

Common Use Cases:
  • Transmission design
  • Performance tuning
  • Mechanical systems
Example:

40-tooth driving gear, 10-tooth driven gear: Ratio = 40/10 = 4:1

Power-to-Weight Ratio

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Power-to-Weight = Engine Power (HP) / Vehicle Weight (lbs)
Metric: Power-to-Weight = Engine Power (kW) / Vehicle Weight (kg)

Description: Measures vehicle performance potential by comparing engine power to vehicle weight.

Standard: Automotive Performance Standards

Accuracy: ±5% depending on measurement precision

Common Use Cases:
  • Performance comparison
  • Racing applications
  • Vehicle analysis
Example:

300 HP engine, 3000 lb car: Ratio = 300/3000 = 0.1 HP/lb

Tire Size Conversion

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Overall Diameter = (Width × Aspect Ratio × 2) / 25.4 + Wheel Diameter
Variables: Width in mm, Aspect Ratio as decimal, Wheel Diameter in inches

Description: Converts between tire size formats and calculates overall wheel diameter.

Standard: Tire and Rim Association Standards

Accuracy: ±1-2mm with standard measurements

Common Use Cases:
  • Tire replacement
  • Speedometer calibration
  • Fitment verification
Example:

225/60R16: Diameter = (225 × 0.60 × 2) / 25.4 + 16 = 26.6 inches

Financial Calculation Formulas

Professional-grade financial formulas for loans, investments, credit analysis, and financial planning.

Credit Utilization Ratio

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Credit Utilization = (Total Credit Card Balances / Total Credit Limits) × 100

Description: Measures percentage of available credit being used, major factor in credit scoring.

Standard: FICO Score Calculation Standards

Accuracy: Exact percentage calculation

Common Use Cases:
  • Credit score improvement
  • Financial health assessment
  • Credit management
Example:

$2,000 balance on $10,000 limit: Utilization = 20%

Debt-to-Income Ratio (DTI)

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DTI = (Total Monthly Debt Payments / Gross Monthly Income) × 100

Description: Assesses borrowing capacity and financial health for lending decisions.

Standard: Consumer Financial Protection Bureau Guidelines

Accuracy: Exact percentage based on reported income

Common Use Cases:
  • Mortgage qualification
  • Credit assessment
  • Financial planning
Example:

Monthly debt $2,000, income $8,000: DTI = 25%

Expense Ratio

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Expense Ratio = (Annual Operating Expenses / Average Net Assets) × 100

Description: Measures annual fees charged by mutual funds or ETFs as percentage of assets.

Standard: Securities and Exchange Commission Standards

Accuracy: Exact calculation based on fund data

Common Use Cases:
  • Investment fund comparison
  • Cost analysis
  • Portfolio optimization
Example:

$1M operating expenses, $100M assets: Expense ratio = 1.00%

Loan Payment Calculator

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M = P × [r(1+r)ⁿ] / [(1+r)ⁿ - 1]
Variables: M = Monthly payment, P = Principal, r = Monthly rate, n = Number of payments

Description: Calculates fixed monthly payments for any type of loan with compound interest.

Standard: Standard Amortization Formula (Banking Industry)

Accuracy: Mathematically exact

Common Use Cases:
  • Mortgage planning
  • Personal loans
  • Business financing
Example:

$200,000 loan, 4% annual rate, 30 years: Monthly payment = $954.83

Return on Investment (ROI)

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ROI = [(Final Value - Initial Value) / Initial Value] × 100
Annualized: Annualized ROI = [(Final Value / Initial Value)^(1/years) - 1] × 100

Description: Measures investment performance and profitability over time periods.

Standard: CFA Institute Financial Analysis Standards

Accuracy: Exact percentage calculation

Common Use Cases:
  • Investment analysis
  • Portfolio performance
  • Business decisions
Example:

Initial: $10,000, Final: $12,000 over 2 years: ROI = 20%, Annualized = 9.54%

Savings Rate Calculation

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Savings Rate = (Monthly Savings / Monthly Income) × 100
Alternative: Savings Rate = [(Income - Expenses) / Income] × 100

Description: Measures percentage of income saved for financial health assessment.

Standard: Personal Finance Industry Standards

Accuracy: Exact percentage based on tracked amounts

Common Use Cases:
  • Financial planning
  • Retirement planning
  • Budget optimization
Example:

$1,000 saved from $5,000 income: Savings rate = 20%

Health & Fitness Formulas

Evidence-based health formulas for fitness assessment, body composition, and wellness calculations.

Body Mass Index (BMI)

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BMI = weight (kg) / height² (m²)
Imperial: BMI = (weight (lbs) / height² (inches)) × 703

Description: Measures body fat based on height and weight to assess healthy weight ranges.

Standard: WHO (World Health Organization) Guidelines

Accuracy: ±2-3% for population screening

Common Use Cases:
  • Health screening
  • Weight management
  • Medical assessments
Example:

Person weighing 70kg, height 1.75m: BMI = 70 / (1.75)² = 22.9

Body Fat Percentage (Navy Method)

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Male: BF% = 495 / (1.0324 - 0.19077 × log(waist - neck) + 0.15456 × log(height)) - 450
Female: BF% = 495 / (1.29579 - 0.35004 × log(waist + hip - neck) + 0.22100 × log(height)) - 450

Description: Estimates body fat percentage using circumference measurements for accurate body composition.

Standard: US Navy Body Composition Assessment Standards

Accuracy: ±3-4% when measured correctly

Common Use Cases:
  • Fitness tracking
  • Military assessments
  • Health monitoring

Calorie Deficit for Weight Loss

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Calorie Deficit = TDEE - Daily Caloric Intake
BMR: TDEE = BMR × Activity Factor
Variables: BMR = (10 × weight) + (6.25 × height) - (5 × age) + s

Description: Calculates calorie deficit needed for safe and sustainable weight loss.

Standard: Mifflin-St Jeor Equation (Gold Standard)

Accuracy: ±10-15% for most individuals

Common Use Cases:
  • Weight loss planning
  • Nutrition coaching
  • Fitness goals
Example:

TDEE 2500 calories, intake 2000 calories: Deficit = 500 calories/day

Waist-to-Hip Ratio (WHR)

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WHR = Waist Circumference / Hip Circumference

Description: Assesses body fat distribution and health risk related to central obesity.

Standard: WHO Health Risk Assessment Guidelines

Accuracy: ±2-3% with proper measurement technique

Common Use Cases:
  • Health risk assessment
  • Body composition analysis
  • Medical screening
Example:

32-inch waist, 38-inch hips: WHR = 32/38 = 0.84

Weight Loss Timeline

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Weeks to Goal = (Current Weight - Target Weight) × 3500 / (Daily Deficit × 7)
Variables: 3500 calories = 1 pound of fat

Description: Estimates realistic timeline for weight loss based on calorie deficit.

Standard: Evidence-based Weight Loss Guidelines

Accuracy: ±2-3 weeks depending on individual factors

Common Use Cases:
  • Goal setting
  • Progress tracking
  • Realistic planning
Example:

Lose 20 lbs with 500 cal/day deficit: 20 × 3500 / (500 × 7) = 20 weeks

Percentage & Change Formulas

Essential percentage calculations for business analytics, academic grading, and mathematical analysis.

Basic Percentage Calculation

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Percentage = (Part / Whole) × 100
Reverse: Part = (Percentage / 100) × Whole

Description: Fundamental percentage calculations for proportions and ratios.

Standard: International Mathematical Standards

Accuracy: Mathematically exact

Common Use Cases:
  • Grade calculations
  • Business analytics
  • Statistical analysis
Example:

45 out of 60: (45/60) × 100 = 75%

Percentage Change

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Percentage Change = [(New Value - Old Value) / Old Value] × 100
Increase: Percentage Increase = [(New - Old) / Old] × 100 (positive result)

Description: Calculates relative change between two values over time.

Standard: Statistical Analysis Standards

Accuracy: Mathematically precise

Common Use Cases:
  • Growth analysis
  • Price changes
  • Performance metrics
Example:

Price changed from $100 to $120: (120-100)/100 × 100 = 20% increase

Discount Calculation

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Discount Amount = Original Price × (Discount Percentage / 100)
Alternative: Sale Price = Original Price × (1 - Discount Percentage / 100)

Description: Calculates discount amounts and final sale prices for retail applications.

Standard: Retail Industry Standards

Accuracy: Mathematically exact

Common Use Cases:
  • Retail pricing
  • Sale calculations
  • Shopping comparisons
Example:

$100 item with 20% discount: Discount = $20, Sale price = $80

Markup Calculation

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Markup Percentage = [(Selling Price - Cost) / Cost] × 100
Alternative: Selling Price = Cost × (1 + Markup Percentage / 100)

Description: Calculates markup percentages and selling prices for business pricing strategies.

Standard: Business Accounting Standards

Accuracy: Mathematically exact

Common Use Cases:
  • Business pricing
  • Profit calculation
  • Retail strategy
Example:

Cost $50, selling $75: Markup = (75-50)/50 × 100 = 50%

Ratio & Proportion Formulas

Mathematical ratio calculations for design, engineering, and proportional analysis.

Aspect Ratio Calculation

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Aspect Ratio = Width : Height (simplified to lowest terms)
Alternative: Aspect Ratio = Width / Height (as decimal)

Description: Calculates proportional relationships for screens, images, and design elements.

Standard: International Standards Organization (ISO)

Accuracy: Mathematically exact

Common Use Cases:
  • Screen design
  • Image scaling
  • Architecture
Example:

1920 × 1080 pixels: Aspect ratio = 16:9 or 1.78:1

Compression Ratio

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Compression Ratio = (Cylinder Volume + Combustion Chamber Volume) / Combustion Chamber Volume
Alternative: CR = Total Volume / Compressed Volume

Description: Measures engine compression for performance and efficiency analysis.

Standard: Society of Automotive Engineers (SAE) Standards

Accuracy: ±0.1 ratio units with precise measurements

Common Use Cases:
  • Engine tuning
  • Performance analysis
  • Fuel requirements
Example:

Total volume 500cc, compressed 50cc: CR = 500/50 = 10:1

Golden Ratio

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Golden Ratio = (a + b) / a = a / b = φ ≈ 1.618
Alternative: φ = (1 + √5) / 2

Description: Calculates the golden ratio for aesthetically pleasing proportions in design.

Standard: Mathematical Constant

Accuracy: Mathematically exact (irrational number)

Common Use Cases:
  • Design layouts
  • Architecture
  • Art composition
Example:

Rectangle: 100 × 61.8 units maintains golden ratio proportions

Proportional Scaling

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New Dimension = Original Dimension × (Target Dimension / Reference Dimension)

Description: Maintains proportional relationships when scaling objects or dimensions.

Standard: Mathematical Proportion Standards

Accuracy: Mathematically exact

Common Use Cases:
  • Image resizing
  • Model scaling
  • Recipe adjustment
Example:

Photo 800×600, scale width to 400: New height = 600 × (400/800) = 300

Formula Standards & Accuracy

Health & Fitness Standards

  • WHO Guidelines: International health organization standards for BMI and health metrics
  • US Navy Method: Proven circumference-based body fat estimation
  • Mifflin-St Jeor: Most accurate BMR calculation method

Financial Standards

  • Banking Industry: Standard amortization and loan calculation methods
  • CFPB Guidelines: Consumer Financial Protection Bureau standards
  • CFA Institute: Professional investment analysis standards

Automotive Standards

  • EPA Standards: Environmental Protection Agency fuel economy methods
  • SAE International: Society of Automotive Engineers technical standards
  • TRA Standards: Tire and Rim Association sizing standards

Mathematical Standards

  • ISO Standards: International organization standardization for ratios and measurements
  • Mathematical Constants: Proven mathematical relationships and formulas
  • Engineering Standards: Professional engineering calculation methods

Accuracy & Precision Notes

All formulas on RatioMath are implemented using double-precision floating-point arithmetic for maximum accuracy. Results are rounded appropriately for practical use while maintaining mathematical precision. Accuracy estimates account for measurement limitations and biological/mechanical variations where applicable.

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