carmath

Methodology

We believe in transparency. Every calculator on CarMath uses documented formulas and clearly stated assumptions. Here's how we do the math.

Our Principles

  • Industry-standard formulas — We use widely accepted calculations, not proprietary black boxes
  • Documented assumptions — We tell you what we're assuming and why
  • Real-world validation — Where possible, we verify against real data
  • Clear limitations — We explain when results are estimates vs. precise calculations

Wheels & Tires

Tire Size & Speedometer

Calculates tire diameter and speedometer error when changing tire sizes.

Formula

Diameter = Wheel + 2 × (Width × Aspect Ratio ÷ 2540)

How It Works

The formula converts tire dimensions to overall diameter. Width is in mm, aspect ratio is a percentage, and wheel diameter is in inches. We multiply by 2 because sidewall height applies to both top and bottom of the tire. The 2540 constant converts mm to inches (25.4) × 100 for the percentage. Speedometer error is calculated as: Error% = ((New Diameter - Old Diameter) / Old Diameter) × 100

Assumptions

  • Tires are measured in standard P-metric format (e.g., 265/70R17)
  • Speedometer is calibrated to OEM tire size
  • Tire wear is not factored in (assumes new tires)

References

Try the Tire Size & Speedometer

Wheel Fitment Calculator

Determines if aftermarket wheels will fit and how much they'll poke or tuck.

Formula

Poke = New Offset - Stock Offset + (New Width - Stock Width) / 2

How It Works

Offset is the distance from the wheel centerline to the mounting surface. A lower offset pushes the wheel outward (more poke). The formula calculates the net change in wheel position relative to the fender. Inner clearance considers: Inner = Stock Inner + (Stock Offset - New Offset) + (New Width - Stock Width) / 2

Assumptions

  • Fender clearance is based on typical vehicle geometry
  • Does not account for suspension modifications
  • Assumes symmetric tire mounting on wheel

References

Try the Wheel Fitment Calculator

Performance

Quarter Mile Predictor

Estimates drag strip ET and trap speed using the classic Hale formula.

Formula

ET = 5.825 × (Weight/HP)^0.333
Trap = 234 × (HP/Weight)^0.333

How It Works

The Hale formula was developed empirically from thousands of drag strip runs. It assumes good traction and driver skill. The 5.825 and 234 constants are calibrated for the 1/4 mile distance. For corrected altitude/temperature, use: Corrected HP = HP × (DA Pressure / 29.92) × (519 / (460 + Temp°F))

Assumptions

  • Driver skill is consistent (no wheel spin, good reaction time)
  • Sea level conditions, 60°F ambient temperature
  • Vehicle launches at optimal RPM
  • Horsepower is measured at the wheels (WHP)

References

Try the Quarter Mile Predictor

Gear Ratio Calculator

Calculates vehicle speed at any RPM based on gearing and tire size.

Formula

Speed = (RPM × Tire Diameter) / (Final Drive × Gear Ratio × 336)

How It Works

The formula solves for speed given engine RPM. The 336 constant comes from: 63,360 inches/mile ÷ 60 min/hour ÷ π = 336.13 Overall ratio = Transmission Gear × Final Drive (axle ratio) For transfer case vehicles: Overall = Trans × T-Case × Axle

Assumptions

  • No tire slip or deformation at speed
  • Tire diameter is static (not accounting for expansion)
  • 336 constant assumes tire diameter in inches, speed in MPH

References

Try the Gear Ratio Calculator

Power-to-Weight Ratio

Compares vehicle performance potential using power-to-weight ratios.

Formula

P/W = Horsepower / (Weight in lbs / 1000)
lbs/hp = Weight / HP

How It Works

Power-to-weight ratio is the simplest performance metric. Higher HP per 1000 lbs = faster acceleration. The lbs/hp format (lower is better) is common in racing. Typical benchmarks: • Economy car: 15-20 lbs/hp • Sports car: 8-12 lbs/hp • Supercar: 4-6 lbs/hp • Top Fuel: <2 lbs/hp

Assumptions

  • Weight includes driver (150 lbs unless specified)
  • Horsepower is crank HP unless noted as WHP
  • Does not account for aerodynamics or gearing

References

Try the Power-to-Weight Ratio

Fuel & HP Specs

Calculates required fuel injector size and airflow for engine builds.

Formula

Injector Flow = (HP × BSFC) / (# Injectors × Duty Cycle)

How It Works

BSFC (Brake Specific Fuel Consumption) measures fuel efficiency at the crankshaft. Lower BSFC = more efficient. Injector sizing ensures adequate fuel delivery at peak power. MAF requirement: CFM = HP × 1.5 (rough estimate) For forced induction, multiply by boost ratio.

Assumptions

  • BSFC of 0.50 lb/hr/hp for naturally aspirated gas engines
  • BSFC of 0.55-0.60 for boosted applications
  • Maximum safe duty cycle is 80-85%

References

Try the Fuel & HP Specs

Engine

Engine Displacement

Calculates total swept volume from bore, stroke, and cylinder count.

Formula

V = (π/4) × Bore² × Stroke × Cylinders

How It Works

Displacement is the total volume swept by all pistons. This formula calculates the volume of a cylinder (πr² × h) multiplied by cylinder count. Unit conversions: • 1 Liter = 1000 cc • 1 Cubic Inch = 16.387 cc • Example: 350 CI = 5,735 cc ≈ 5.7L

Assumptions

  • All cylinders are identical in bore and stroke
  • Does not include combustion chamber volume (just swept)
  • Bore and stroke in same units (mm or inches)

References

  • SAE J1349 - Engine Displacement Measurement
Try the Engine Displacement

Cylinder Overbore

Calculates displacement gain and safety considerations when boring cylinders.

Formula

New Displacement = π/4 × (Bore + Overbore)² × Stroke × Cyl

How It Works

Overboring increases cylinder diameter to clean up wear or fit larger pistons. Each 0.5mm overbore removes 0.25mm of wall thickness per side. Common overbore sizes: • .020" (0.5mm) - Standard cleanup • .030" (0.76mm) - Common rebuild • .040" (1.0mm) - Near maximum for most blocks • .060" (1.5mm) - Requires sonic testing

Assumptions

  • Standard cleanup bore is 0.5mm (0.020")
  • Maximum safe overbore depends on block construction
  • Wall thickness must be verified before machining

References

Try the Cylinder Overbore

Off-Road

Crawl Ratio Calculator

Calculates overall gear reduction for rock crawling and off-road.

Formula

Crawl Ratio = Trans Low × T-Case Low × Axle Ratio

How It Works

Crawl ratio determines how slowly you can move while maintaining torque. Higher ratios allow better control on steep obstacles. Benchmarks: • Stock Jeep Wrangler: ~40:1 • Built rock crawler: 80-100:1 • Competition: 150:1+ Ground speed at 1000 RPM = (Tire Circumference × 60) / (Crawl Ratio × 1056)

Assumptions

  • All gear ratios are at their lowest setting
  • Does not account for tire diameter (affects ground speed)
  • Higher crawl ratio = more torque multiplication

References

Try the Crawl Ratio Calculator

Regear Calculator

Calculates optimal axle ratio after changing tire size.

Formula

New Ratio = Stock Ratio × (New Tire Diameter / Stock Tire Diameter)

How It Works

Larger tires act like a taller gear, lowering RPM. Regearing restores the original engine operating point. Example: Stock 3.73 gears with 33" tires instead of 30" New ratio = 3.73 × (33/30) = 4.10 (closest available: 4.10 or 4.11)

Assumptions

  • Goal is to restore stock RPM at highway speed
  • Does not account for speedometer correction
  • Available gear sets may not match exact calculated ratio

References

Try the Regear Calculator

Towing

Towing & Payload Margin

Calculates real-world towing capacity after accounting for actual loads.

Formula

Available Payload = GVWR - Curb Weight - Passengers - Cargo

How It Works

Manufacturers often advertise "maximum" towing capacity with no passengers or cargo. Real-world capacity is significantly lower. Key limits to check: • GVWR (Gross Vehicle Weight Rating) • GAWR (Gross Axle Weight Rating) • GCWR (Gross Combined Weight Rating) • Tongue weight limit

Assumptions

  • Passenger weight defaults to 150 lbs each
  • Tongue weight is 10-15% of trailer weight
  • GVWR is the legal maximum, not recommended operating weight

References

Try the Towing & Payload Margin

Buying & Selling

Out-the-Door Price

Calculates the true total cost of a vehicle purchase.

Formula

OTD = Vehicle Price - Trade-in + Sales Tax + Doc Fee + Title + Registration

How It Works

The "out-the-door" price is what you actually pay. It includes all taxes, fees, and charges. Always negotiate based on OTD, not sticker price. Common hidden fees to watch for: • Dealer prep fee • Advertising fee • VIN etching • Fabric protection

Assumptions

  • Sales tax applies to (Vehicle Price - Trade-in) in most states
  • Doc fees vary by dealer ($0-$999 typical)
  • Some states have no sales tax on vehicles

References

Try the Out-the-Door Price

Depreciation Curve

Projects vehicle value over time using depreciation curves.

Formula

Value = MSRP × (1 - Annual Rate)^Years

How It Works

Depreciation follows an exponential decay curve, steepest in the first few years. The "value floor" occurs when depreciation flattens and the vehicle trades as a used commodity. Sweet spot for buying used: 3-5 years old, after steepest depreciation but before major repairs.

Assumptions

  • Average car loses 15-20% in year 1, 10-15% annually after
  • Luxury vehicles depreciate faster than economy cars
  • Trucks and SUVs often hold value better

References

Try the Depreciation Curve

Private Sale Price

Determines optimal asking price for private party vehicle sales.

Formula

List Price = Market Value × Condition Factor + Upgrades Value × 0.5

How It Works

Private sale pricing should fall between trade-in value (dealer pays you) and retail value (you pay dealer). Upgrades add perceived value but rarely recover full cost. Pricing strategy: • List 10-15% above target price for negotiation room • Excellent condition commands premium • High mileage reduces value more than age

Assumptions

  • Private sale typically 10-20% below dealer retail
  • Modifications rarely add full value
  • Condition has significant impact (±20%)

References

Try the Private Sale Price

Budget

Repair vs Replace

Helps decide whether to repair your current car or buy a replacement.

Formula

Keep if: Repair Cost < (Replacement Cost - Current Value) × Months Remaining / 12

How It Works

This is a pure financial analysis. The calculation compares the cost per month of repairing vs replacing over the expected ownership period. Consider non-financial factors: • Safety features of newer vehicles • Fuel efficiency improvements • Reliability and peace of mind

Assumptions

  • Replacement cost includes tax, registration, and insurance changes
  • Repair provides estimated months of reliable service
  • Does not factor in emotional attachment or preference

References

Try the Repair vs Replace

Beater Break-Even

Calculates how long a cheap car must last to beat financing a nicer one.

Formula

Break-Even Months = Financed Car Payments × Months / Beater Total Cost

How It Works

A $3,000 beater that lasts 18 months costs $167/month. If a financed car would cost $400/month, the beater saves $233/month. Even with $1,500 in repairs, it may still win. Risk factors: • Unreliable transportation affects income • Safety concerns with older vehicles • Stress of frequent breakdowns

Assumptions

  • Beater cost includes purchase, repairs, and higher maintenance
  • Insurance and registration may differ between vehicles
  • Opportunity cost of cash not considered

References

Try the Beater Break-Even

Everyday

Commute Cost Calculator

Calculates the true monthly cost of your daily commute.

Formula

Monthly Cost = (Miles / MPG × $/Gallon) + (Miles × Maintenance/Mile) + Parking + Tolls

How It Works

Commuting costs more than just gas. Factor in wear and tear, parking, tolls, and time value. IRS 2024 standard mileage rate: 67 cents/mile This includes: gas, depreciation, maintenance, insurance, registration

Assumptions

  • Maintenance cost estimated at $0.05-0.10/mile
  • Depreciation included in IRS mileage rate ($0.67/mile for 2024)
  • Insurance is fixed regardless of mileage

References

Try the Commute Cost Calculator

Gas Station Detour

Determines if driving further for cheaper gas is worth it.

Formula

Savings = (Gallons × Price Diff) - (Extra Miles / MPG × Local Price)

How It Works

A 10-cent/gallon savings on 15 gallons = $1.50. If the detour is 4 miles extra at 25 MPG and $3.50/gallon, it costs $0.56. Net savings: $0.94. Rule of thumb: Rarely worth it for less than $0.10/gallon difference unless you're already driving past.

Assumptions

  • Round trip distance for the detour
  • Time value not included (only fuel cost)
  • Tank is filled completely at the cheaper station

References

Try the Gas Station Detour

Road Trip Fuel Planner

Estimates fuel stops, costs, and time for long road trips.

Formula

Total Fuel Cost = Total Distance / MPG × Price per Gallon

How It Works

Plan fuel stops before you need them. Don't rely on finding gas at empty—rural areas may have 50+ mile gaps. Tips: • Fill up before crossing into high-tax states • Apps like GasBuddy show prices along route • Consider fuel rewards programs for regular routes

Assumptions

  • Highway MPG may differ from combined rating
  • Fuel prices vary by state and location
  • Tank range calculated with 10% reserve

References

Try the Road Trip Fuel Planner

Mechanics

Torque-Angle Converter

Calculates final bolt tension from torque-plus-angle specifications.

Formula

Final Stretch = Base Torque + (Angle × Thread Pitch / 360)

How It Works

Torque-to-yield (TTY) bolts are intentionally stretched to their yield point for maximum clamping force. They cannot be reused. Common TTY applications: • Cylinder head bolts • Main bearing cap bolts • Connecting rod bolts • Flywheel bolts (some applications)

Assumptions

  • Bolt is not yielded (still in elastic range)
  • Threads are clean and lubricated per spec
  • Torque wrench is calibrated

References

Try the Torque-Angle Converter

AC Refrigerant Charge

Calculates correct refrigerant charge after AC component replacement.

Formula

Adjusted Charge = Base Charge + Condenser Adder + Line Length Adder

How It Works

Refrigerant charge is critical for AC performance and compressor longevity. Overcharge causes high head pressure; undercharge causes poor cooling and potential compressor damage. Typical charges: • Compact cars: 14-18 oz • Sedans: 20-28 oz • Trucks/SUVs: 28-40 oz

Assumptions

  • System is properly evacuated and leak-free
  • Correct refrigerant type (R134a, R1234yf)
  • Adjustments based on manufacturer guidelines

References

Try the AC Refrigerant Charge

Battery CCA Calculator

Determines cold cranking amps needed for your engine and climate.

Formula

Required CCA = Engine CI × Temperature Factor + Accessory Load

How It Works

CCA measures battery power at cold temperatures. Rule of thumb: 1 CCA per cubic inch of engine displacement, adjusted for temperature. Temperature factors: • 80°F: Battery at 100% capacity • 32°F: Battery at ~65% capacity • 0°F: Battery at ~40% capacity

Assumptions

  • CCA rating is at 0°F (-18°C)
  • Larger engines require more cranking power
  • Diesel engines need ~200% more CCA than gas

References

Try the Battery CCA Calculator

Trucking

Cost Per Mile (Trucking)

Calculates true operating cost per mile for owner-operators.

Formula

CPM = (Fixed Costs / Monthly Miles) + (Fuel + Maintenance + Tires per Mile)

How It Works

Cost per mile determines profitability. If your CPM is $1.50 and you get paid $2.00/mile, profit is $0.50/mile. Typical breakdown: • Fuel: 30-40% of costs • Truck payment: 15-25% • Insurance: 5-10% • Maintenance: 10-15% • Driver pay: 25-35%

Assumptions

  • Fixed costs include: insurance, permits, truck payment, parking
  • Variable costs include: fuel, maintenance, tires, tolls
  • Driver pay not included in operating cost

References

Try the Cost Per Mile (Trucking)

Found an Error?

If you believe one of our calculations is wrong or could be improved, please let us know. We take accuracy seriously and will investigate any reported issues.