Convert horsepower to BTU / hour
Learn how to convert
1
horsepower to
BTU / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(horsepower\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(watt\right)\)
\(\text{Left side: 1.0 } \left(horsepower\right) = {\color{rgb(89,182,91)} 745.699872\left(watt\right)} = {\color{rgb(89,182,91)} 745.699872\left(W\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{BTU}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{1055.05585262}{3.6 \times 10^{3}}\left(watt\right)} = {\color{rgb(125,164,120)} \dfrac{1055.05585262}{3.6 \times 10^{3}}\left(W\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(horsepower\right)={\color{rgb(20,165,174)} x}\left(\dfrac{BTU}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 745.699872} \times {\color{rgb(89,182,91)} \left(watt\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1055.05585262}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(watt\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 745.699872} \cdot {\color{rgb(89,182,91)} \left(W\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1055.05585262}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(W\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 745.699872} \cdot {\color{rgb(89,182,91)} \cancel{\left(W\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1055.05585262}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(W\right)}}\)
\(\text{Conversion Equation}\)
\(745.699872 = {\color{rgb(20,165,174)} x} \times \dfrac{1055.05585262}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1055.05585262}{3.6 \times 10^{3}} = 745.699872\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{1055.05585262}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1055.05585262}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{1055.05585262} = 745.699872 \times \dfrac{3.6 \times 10^{3}}{1055.05585262}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1055.05585262}} \times {\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(166,218,227)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{1055.05585262}}} = 745.699872 \times \dfrac{3.6 \times 10^{3}}{1055.05585262}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{745.699872 \times 3.6 \times 10^{3}}{1055.05585262}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx2544.4335791\approx2.5444 \times 10^{3}\)
\(\text{Conversion Equation}\)
\(1.0\left(horsepower\right)\approx{\color{rgb(20,165,174)} 2.5444 \times 10^{3}}\left(\dfrac{BTU}{hour}\right)\)
