Avoided exhaust-air heating cost calculator

The 60 converts airflow per minute to airflow per hour; divide useful heat by heater efficiency.

Units

S_{h} = \frac{\dot{V} \times 60 \times \rho \times c_{p} \times T_{i} - T_{o} \times h_{\text{saved}} \times c_{f}}{\eta_{h}}

Calculator

Enter the values you know and leave one box empty. Calculate finds the empty one, the result or any input.

Given

S_{h} = \frac{4200 \times 60 \times 0.075 \times 0.24 \times 34 \times 900 \times 0.000013}{0.82} \approx 2{,}201

Symbol	Meaning	Unit
$S_{h}$	heating cost saved	$/yr
$\dot{V}$	airflow	ft³/min
$\rho$	air density; 0.075 in the example	lb/ft³
$c_{p}$	specific heat; 0.24 in the example	Btu/(lb·°F)
$T_{i} - T_{o}$	indoor minus outdoor temperature	°F
$h_{\text{saved}}$	avoided exhaust hours	h/yr
$c_{f}$	fuel price per Btu	$/Btu
$\eta_{h}$	heating efficiency	fraction

Symbol	Meaning	Unit
$S_{h}$	heating cost saved	$/yr
$\dot{V}$	airflow	L/s
$\rho$	air density	kg/m³
$c_{p}$	specific heat	kJ/(kg·K)
$T_{i} - T_{o}$	indoor minus outdoor temperature	K
$h_{\text{saved}}$	avoided exhaust hours	h/yr
$c_{f}$	fuel-energy price per kilowatt-hour	$/kWh
$\eta_{h}$	heating efficiency	fraction

Results are estimates for study and screening. Check the inputs, units and assumptions before you use them for design, billing or contract decisions.