WattMath

Our Methodology

Transparency in how we calculate results. No black boxes, no hidden assumptions.

General Approach

Our calculators use industry-standard formulas and conservative assumptions. We prioritize accuracy over optimism—you'll get realistic estimates rather than best-case scenarios designed to sell products.

Solar & EV Calculators

Solar Panel Payback Calculator

Core Formulas

Daily Production (kWh) = System Size (kW) × Peak Sun Hours × Efficiency Factor
Annual Production = Daily Production × 365
Tax Credit = System Cost × Tax Credit %
Net Cost = System Cost - Tax Credit
Annual Savings = Annual Production × Electricity Rate × (1 + Rate Increase)^year
Payback = Years until cumulative savings ≥ Net Cost

Key Assumptions

  • Panel Degradation: 0.5% per year (industry standard warranty assumption)
  • System Efficiency: Default 80%, accounts for inverter losses, wiring, shading, and derating factors
  • Tax Credit: Federal ITC at 30% through 2032, stepping down thereafter
  • Rate Increases: Default 2.5% annual electricity rate increase (historical average)
  • CO₂ Offset: 0.417 kg CO₂ per kWh (EPA average US grid emission factor)

Data Sources

  • NREL PVWatts for solar irradiance data
  • EIA for average electricity rates
  • EnergySage for typical system costs

EV Charging Cost Calculator

Core Formulas

Annual kWh = Annual Miles / Efficiency (miles/kWh)
Home kWh = Annual kWh × Home Charging %
Public kWh = Annual kWh × (1 - Home Charging %)
EV Annual Cost = (Home kWh × Home Rate) + (Public kWh × Public Rate)
Gas Annual Cost = (Annual Miles / MPG) × Gas Price
Equivalent MPG = Gas MPG × (Gas Cost / EV Cost)

Key Assumptions

  • Charging Losses: ~10-15% efficiency loss during charging (built into EPA efficiency ratings)
  • Default Efficiency: 3.5 miles/kWh (typical for modern EVs)
  • Usable Battery: 80% depth of discharge for charging session estimates
  • CO₂ Emissions: Gas emits 19.6 lbs CO₂ per gallon
  • Public Charging: Rates vary $0.30-$0.50/kWh typical for DC fast charging

Solar Panel Sizing Calculator

Core Formulas

Annual Usage (kWh) = Monthly Usage × 12
Required Production = Annual Usage × Offset Target %
System Size (kW) = Required Production / (365 × Sun Hours × Efficiency)

Number of Panels = System Size / Panel Wattage (kW)
Roof Space Required = Number of Panels × 17.5 sq ft

Daily Production = System Size × Sun Hours × Efficiency
Annual Production = Daily Production × 365
Annual Savings = min(Annual Production, Annual Usage) × Electricity Rate

Key Assumptions

  • Panel Size: Average panel requires 17.5 sq ft of roof space
  • System Efficiency: 75-85% typical, accounting for inverter, wiring, temperature, and shading losses
  • Offset Target: 100% covers current usage; 110-125% accounts for future EV or expansion
  • Cost Range: $2.50-$3.50 per watt installed (before incentives)
  • Panel Options: 350W (standard), 400W (premium), 450W (high-efficiency), 500W (commercial)

Heating Calculators

Heat Pump vs Furnace Calculator

Core Formulas

Heating Load (BTU) = Heating Therms × 100,000 BTU/therm
Heat Pump kWh = Heating Load / (HSPF × 1000)
Heat Pump Cost = kWh × Electricity Rate

Furnace Therms = Heating Therms / Efficiency
Natural Gas Cost = Therms × $/therm
Propane Gallons = (Therms × 100,000) / 91,500 BTU/gallon
Oil Gallons = (Therms × 100,000) / 138,500 BTU/gallon

Cooling: AC uses ~14% more electricity than heat pump (SEER 14 vs 16)
15-Year Cost = Equipment Cost + (Annual Operating × 15)

Key Assumptions

  • HSPF: Heating Seasonal Performance Factor (8-12 typical, higher is more efficient)
  • Cold Climate: Heat pump efficiency decreases below 25°F; backup heat may be needed
  • BTU Values: Natural gas: 100,000 BTU/therm; Propane: 91,500 BTU/gallon; Oil: 138,500 BTU/gallon
  • Home Size Presets: Based on typical heating loads for moderate climate zones
  • Cooling: Heat pumps (SEER 16) vs standard AC (SEER 14) comparison included

Space Heater vs Central Heat Calculator

Core Formulas

Heater kWh/month = (Watts × Hours/day × Days × Quantity) / 1000
Heater Cost = kWh × Electricity Rate
Heater BTU/hour = Watts × 3.412 BTU/Watt

Equivalent Fuel = BTU Output / (Furnace Efficiency × BTU per unit)
Fuel Cost = Fuel Needed × Fuel Rate

Zone Heating Benefit = (1 - Room Size / Home Size) × 100%
Break-even Rate = Fuel cost for same BTU / kWh used

Key Assumptions

  • Electric Conversion: 1 watt = 3.412 BTU/hour (100% conversion efficiency)
  • Zone Heating: Space heaters only heat occupied room; central heat warms entire home
  • Heating Season: ~4 months for annual savings calculation

Steam Pipe Heat Loss Calculator

Core Formulas

Bare Pipe Surface Area = π × Diameter × Length
Bare Loss/ft = Coefficient × π × (Diameter/12) × (Steam Temp - Ambient)
Bare Total Loss = Loss/ft × Length (BTU/hr)

Insulated Loss/ft = (2π × k-value × ΔT) / ln(Outer Diameter / Pipe Diameter) / 12
Heat Reduction % = (Bare Loss - Insulated Loss) / Bare Loss × 100

Annual BTU = Hourly Loss × Operating Hours
Steam Saved (lbs) = BTU Saved / 1,000
Annual Savings = (Steam Saved / 1,000) × $/1000 lbs
Payback = Insulation Cost / Annual Savings
CO₂ Saved = (MMBTU Saved) × 117 lbs (natural gas boiler)

Key Assumptions

  • Heat Transfer Coefficients: Vary by pipe diameter (1.3-2.0 BTU/hr/ft²/°F for bare pipe)
  • Insulation k-values: Fiberglass: 0.25; Mineral wool: 0.27; Calcium silicate: 0.35; Cellular glass: 0.30 BTU·in/hr·ft²/°F
  • Steam Equivalent: 1,000 BTU ≈ 1 lb of steam at atmospheric pressure
  • Insulation Cost: Estimated $8-16/linear foot installed depending on thickness

Data Sources

  • ASHRAE Fundamentals for heat transfer coefficients
  • 3E Plus (DOE) for insulation thermal conductivity values

Power & Motor Calculators

Electric Motor Torque & HP Calculator

Core Formulas

HP = (Torque × RPM) / 5252
Torque (lb-ft) = (HP × 5252) / RPM
RPM = (HP × 5252) / Torque

Power (Watts) = HP × 745.7
Power (kW) = Watts / 1000
Torque (N·m) = Torque (lb-ft) × 1.3558
Angular Velocity (rad/s) = (RPM × 2π) / 60

Full Load Current (3-phase) = (HP × 746) / (Voltage × √3 × PF × Efficiency)

Key Assumptions

  • The 5252 Constant: Derived from 33,000 ft-lb/min per HP ÷ 2π radians/revolution
  • Full Load Current: Assumes 480V, 3-phase, 85% power factor, 90% efficiency
  • Synchronous Speeds (60 Hz): 2-pole: 3600 RPM; 4-pole: 1800 RPM; 6-pole: 1200 RPM; 8-pole: 900 RPM

Generator Sizing Calculator

Approach

Running Watts = Σ (Each Load's Running Watts × Quantity)
Starting Watts = Running of other loads + Largest single starting load
Peak Watts = Max of (Total Running, Starting scenario)

Recommended Size = Peak Watts × 1.20 safety margin
Fuel Consumption ≈ kW × 0.1 gallons/hour at 50% load

Key Assumptions

  • Motor Starting: Motors require 2-3× running watts to start
  • Safety Margin: 20% added to peak calculation
  • Staggered Starting: Assumes largest motor starts last while others run
  • Fuel Estimate: Rough approximation; actual varies by load and generator efficiency

Wire Gauge & Voltage Drop Calculator

Core Formulas

Wire Resistance (Ω) = (Resistance per 1000 ft × Distance × Multiplier) / 1000
  - Single Phase Multiplier: 2 (round trip)
  - Three Phase Multiplier: 1.732 (√3)

Voltage Drop (V) = Current (A) × Wire Resistance (Ω)
Voltage Drop % = (Voltage Drop / System Voltage) × 100
Voltage at Load = System Voltage - Voltage Drop
Power Loss (W) = Voltage Drop × Current

Wire Resistance Values (Ohms per 1000 ft at 75°C)

  • Copper: 14 AWG: 3.14; 12: 1.98; 10: 1.24; 8: 0.778; 6: 0.491; 4: 0.308; 2: 0.194; 1/0: 0.122; 4/0: 0.0608
  • Aluminum: Approximately 1.6× copper resistance (requires larger gauge for same ampacity)

Key Assumptions

  • NEC Guidelines: 3% max voltage drop for branch circuits; 5% total (feeder + branch)
  • Temperature: Resistance values at 75°C conductor temperature
  • Ampacity: This calculator focuses on voltage drop; verify ampacity separately per NEC Table 310.16
  • Distance: One-way distance from panel to load; calculator accounts for round-trip

Data Sources

  • NEC (National Electrical Code) Table 8 for conductor resistance
  • IEEE standards for voltage drop recommendations

Efficiency Calculators

Appliance Energy Payback Calculator

Core Formulas

Annual Hours = Hours × (365 for daily | 52 for weekly | 12 for monthly)
Annual kWh = (Wattage × Annual Hours) / 1000
Annual Cost = Annual kWh × Electricity Rate

Energy Saved = Old kWh - New kWh
Annual Savings = Old Cost - New Cost
Payback = Appliance Cost / Annual Savings
Efficiency Improvement = (Old Watts - New Watts) / Old Watts × 100%
CO₂ Saved = kWh Saved × 0.92 lbs/kWh

Key Assumptions

  • Wattage: Nameplate ratings; actual varies with usage
  • Refrigerators: Run intermittently; duty cycle factored into typical wattage
  • Appliance Lifespan: 15 years typical for long-term calculations
  • CO₂ Factor: 0.92 lbs CO₂ per kWh (US average grid)

Vampire Load Auditor

Core Formula

Per Device:
  Total Watts = Standby Watts × Quantity
  Annual kWh = (Total Watts × 24 × 365) / 1000
  Annual Cost = kWh × Electricity Rate

Totals:
  Total kWh = Σ (All device kWh)
  Total Cost = Σ (All device costs)
  CO₂ Emissions = Total kWh × 0.92 lbs/kWh
  Lightbulb Equivalent = Total kWh × 1000 / 10W

Data Sources

  • Lawrence Berkeley National Laboratory standby power database
  • ENERGY STAR product specifications

Typical Standby Power Values

  • TV (LED): 5W; TV (Plasma): 15W
  • Gaming Console: 10W; Cable/DVR Box: 20-25W
  • Computer: 5W; Monitor: 3W
  • Phone/Tablet Charger: 2W; Laptop Charger: 4W
  • Router/Modem: 10W; Smart Speaker: 3W

Lighting Retrofit ROI Calculator

Core Formulas

Per Fixture:
  Old kWh = (Old Watts × Quantity × Hours/day × Days/year) / 1000
  New kWh = (New Watts × Quantity × Hours/day × Days/year) / 1000

Total kWh Saved = Σ (Old kWh - New kWh)
Annual Savings = kWh Saved × Electricity Rate
Project Cost = (LED Cost + Labor Cost) × Total Fixtures
Payback = Project Cost / Annual Savings
10-Year ROI = ((Savings × 10) - Project Cost) / Project Cost × 100%
CO₂ Saved = kWh Saved × 0.92 lbs/kWh

Common Retrofit Scenarios

  • T8 Fluorescent (32W) → LED (15W): 53% reduction
  • T12 Fluorescent (40W) → LED (18W): 55% reduction
  • Incandescent (60W) → LED (9W): 85% reduction
  • Metal Halide (400W) → LED (150W): 63% reduction
  • High Pressure Sodium (250W) → LED (100W): 60% reduction

Insulation ROI Calculator

Core Formulas

Heat Loss Reduction % = (New R-Value - Current R-Value) / New R-Value × 100

Area Impact Factors (portion of HVAC affected):
  Attic: 25% heating, 35% cooling
  Walls: 20% heating, 15% cooling
  Floor: 10% heating, 5% cooling
  Basement: 15% heating, 8% cooling

Climate Multipliers:
  Cold climate: 1.3× heating impact
  Hot climate: 1.3× cooling impact

Annual Savings = (Heating Cost × Heating Factor × Reduction) + (Cooling Cost × Cooling Factor × Reduction)
Upgrade Cost = Square Footage × Cost per sq ft
Payback Years = Upgrade Cost / Annual Savings
10-Year ROI = ((Annual Savings × 10) - Upgrade Cost) / Upgrade Cost × 100%

Key Assumptions

  • R-Value Recommendations: Attic: R-38 to R-60; Walls: R-13 to R-21; Floors: R-25 to R-30
  • Cost Estimates: Attic: $1.50/sq ft; Walls: $3.50/sq ft; Floor: $2.00/sq ft; Basement: $2.50/sq ft
  • Existing R-Values: Uninsulated: R-3 (framing only); Common existing: R-11, R-19, R-30
  • Air Sealing: Not included; can add 25-40% additional savings when done with insulation

Data Sources

  • DOE Insulation Fact Sheet for R-value recommendations by climate zone
  • ENERGY STAR for typical savings percentages

Smart Thermostat Savings Calculator

Core Formulas

Base Savings = 8% (EPA average for smart thermostats)

Thermostat Upgrade Bonus:
  From manual: +4%
  From basic programmable: -2%

Feature Savings (% of HVAC cost):
  Geofencing: 3%
  Learning Algorithm: 2%
  Smart Scheduling: 2-8% (based on occupancy pattern)
  Remote Control: 1.5%
  Energy Insights: 1%
  Zone Control (if applicable): 5%

Total Savings % = min(Sum of all features, 25%)  // Capped at 25%
Annual Savings = HVAC Cost × Total Savings %
Payback Months = Thermostat Cost / (Annual Savings / 12)
5-Year Net Savings = (Annual Savings × 5) - Thermostat Cost

Key Assumptions

  • EPA Baseline: 8% average savings from smart thermostats (ENERGY STAR certified)
  • Occupancy Impact: Away during work: 5%; Extended travel: 8%; Variable: 6%; Home most: 2%
  • Maximum Savings: Capped at 25% to avoid unrealistic projections
  • Popular Models: Nest ($130-250), Ecobee ($170-250), Honeywell ($150-200)
  • Utility Rebates: Many utilities offer $50-100 rebates (not included in calculations)

Data Sources

  • EPA ENERGY STAR program for baseline savings data
  • Nest Labs and Ecobee published efficiency studies

Limitations & Disclaimers

  • All calculations are estimates for planning purposes
  • Actual results depend on installation quality, local conditions, and usage patterns
  • Energy prices fluctuate; use current rates from your utility
  • Climate significantly affects heating/cooling calculations—our defaults assume moderate climates
  • Always consult qualified professionals for major investments
  • Tax advice should come from a qualified tax professional
  • Environmental impact calculations use national averages; your local grid may differ

Feedback

Found an error in our methodology? Have suggestions for improvement? We welcome feedback from engineers, energy professionals, and users. Contact us with your input.