Heat Index worksheet

1. Heat index (feels like): 37.7 °C

1. The weather service's formulas use °F, so convert first: °C × 9/5 + 32

   $32\text{\hspace{0.17em}°C}\times \frac{9}{5}+32$$=89.6\text{\hspace{0.17em}°F}$

2. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(89.6+61+1.2\times \left(89.6-68\right)+0.094\times 62\right)$$=91.174\text{\hspace{0.17em}°F}$

3. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{91.174+89.6}{2}$$=90.387\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

4. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 89.6+10.14333127\times 62+\mathrm{-0.22475541}\times 89.6\times 62+\mathrm{-0.00683783}\times \mathrm{8,028.16}+\mathrm{-0.05481717}\times \mathrm{3,844}+0.00122874\times \mathrm{8,028.16}\times 62+0.00085282\times 89.6\times \mathrm{3,844}+\mathrm{-0.00000199}\times \mathrm{8,028.16}\times \mathrm{3,844}$$=99.84439624\text{\hspace{0.17em}°F}$

5. Convert the heat index back to Celsius: (°F − 32) × 5/9

   $\left(99.84439624\text{\hspace{0.17em}°F}-32\right)\times \frac{5}{9}$$=37.69133125\text{\hspace{0.17em}°C}$

2. Heat index (feels like): 28.3 °C

1. The weather service's formulas use °F, so convert first: °C × 9/5 + 32

   $28\text{\hspace{0.17em}°C}\times \frac{9}{5}+32$$=82.4\text{\hspace{0.17em}°F}$

2. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(82.4+61+1.2\times \left(82.4-68\right)+0.094\times 48\right)$$=82.596\text{\hspace{0.17em}°F}$

3. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{82.596+82.4}{2}$$=82.498\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

4. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 82.4+10.14333127\times 48+\mathrm{-0.22475541}\times 82.4\times 48+\mathrm{-0.00683783}\times \mathrm{6,789.76}+\mathrm{-0.05481717}\times \mathrm{2,304}+0.00122874\times \mathrm{6,789.76}\times 48+0.00085282\times 82.4\times \mathrm{2,304}+\mathrm{-0.00000199}\times \mathrm{6,789.76}\times \mathrm{2,304}$$=82.89471756\text{\hspace{0.17em}°F}$

5. Convert the heat index back to Celsius: (°F − 32) × 5/9

   $\left(82.89471756\text{\hspace{0.17em}°F}-32\right)\times \frac{5}{9}$$=28.27484309\text{\hspace{0.17em}°C}$

3. Heat index (feels like): 86 °F

1. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(82+61+1.2\times \left(82-68\right)+0.094\times 68\right)$$=83.096\text{\hspace{0.17em}°F}$

2. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{83.096+82}{2}$$=82.548\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

3. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 82+10.14333127\times 68+\mathrm{-0.22475541}\times 82\times 68+\mathrm{-0.00683783}\times \mathrm{6,724}+\mathrm{-0.05481717}\times \mathrm{4,624}+0.00122874\times \mathrm{6,724}\times 68+0.00085282\times 82\times \mathrm{4,624}+\mathrm{-0.00000199}\times \mathrm{6,724}\times \mathrm{4,624}$$=86.00711326\text{\hspace{0.17em}°F}$

4. Heat index (feels like): 166.4 °F

1. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(105+61+1.2\times \left(105-68\right)+0.094\times 70\right)$$=108.49\text{\hspace{0.17em}°F}$

2. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{108.49+105}{2}$$=106.745\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

3. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 105+10.14333127\times 70+\mathrm{-0.22475541}\times 105\times 70+\mathrm{-0.00683783}\times \mathrm{11,025}+\mathrm{-0.05481717}\times \mathrm{4,900}+0.00122874\times \mathrm{11,025}\times 70+0.00085282\times 105\times \mathrm{4,900}+\mathrm{-0.00000199}\times \mathrm{11,025}\times \mathrm{4,900}$$=166.4085258\text{\hspace{0.17em}°F}$

5. Heat index (feels like): 81.3 °F

1. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(80+61+1.2\times \left(80-68\right)+0.094\times 55\right)$$=80.285\text{\hspace{0.17em}°F}$

2. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{80.285+80}{2}$$=80.1425\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

3. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 80+10.14333127\times 55+\mathrm{-0.22475541}\times 80\times 55+\mathrm{-0.00683783}\times \mathrm{6,400}+\mathrm{-0.05481717}\times \mathrm{3,025}+0.00122874\times \mathrm{6,400}\times 55+0.00085282\times 80\times \mathrm{3,025}+\mathrm{-0.00000199}\times \mathrm{6,400}\times \mathrm{3,025}$$=81.290103\text{\hspace{0.17em}°F}$

6. Heat index (feels like): 75.5 °F

1. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(75+61+1.2\times \left(75-68\right)+0.094\times 70\right)$$=75.49\text{\hspace{0.17em}°F}$

2. Average it with the air reading. That's below 80 °F, so the quick estimate is the heat index

   $\frac{75.49+75}{2}$$=75.245\text{\hspace{0.17em}°F}$$=\text{< 80}$

7. Heat index (feels like): 442.2 °F

1. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(130+61+1.2\times \left(130-68\right)+0.094\times 90\right)$$=136.93\text{\hspace{0.17em}°F}$

2. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{136.93+130}{2}$$=133.465\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

3. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 130+10.14333127\times 90+\mathrm{-0.22475541}\times 130\times 90+\mathrm{-0.00683783}\times \mathrm{16,900}+\mathrm{-0.05481717}\times \mathrm{8,100}+0.00122874\times \mathrm{16,900}\times 90+0.00085282\times 130\times \mathrm{8,100}+\mathrm{-0.00000199}\times \mathrm{16,900}\times \mathrm{8,100}$$=442.1979932\text{\hspace{0.17em}°F}$

8. Heat index (feels like): 182 °F

1. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(110+61+1.2\times \left(110-68\right)+0.094\times 65\right)$$=113.755\text{\hspace{0.17em}°F}$

2. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{113.755+110}{2}$$=111.8775\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

3. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 110+10.14333127\times 65+\mathrm{-0.22475541}\times 110\times 65+\mathrm{-0.00683783}\times \mathrm{12,100}+\mathrm{-0.05481717}\times \mathrm{4,225}+0.00122874\times \mathrm{12,100}\times 65+0.00085282\times 110\times \mathrm{4,225}+\mathrm{-0.00000199}\times \mathrm{12,100}\times \mathrm{4,225}$$=182.0060701\text{\hspace{0.17em}°F}$

9. Heat index (feels like): 30.3 °C

1. The weather service's formulas use °F, so convert first: °C × 9/5 + 32

   $30\text{\hspace{0.17em}°C}\times \frac{9}{5}+32$$=86\text{\hspace{0.17em}°F}$

2. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(86+61+1.2\times \left(86-68\right)+0.094\times 45\right)$$=86.415\text{\hspace{0.17em}°F}$

3. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{86.415+86}{2}$$=86.2075\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

4. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 86+10.14333127\times 45+\mathrm{-0.22475541}\times 86\times 45+\mathrm{-0.00683783}\times \mathrm{7,396}+\mathrm{-0.05481717}\times \mathrm{2,025}+0.00122874\times \mathrm{7,396}\times 45+0.00085282\times 86\times \mathrm{2,025}+\mathrm{-0.00000199}\times \mathrm{7,396}\times \mathrm{2,025}$$=86.5692391\text{\hspace{0.17em}°F}$

5. Convert the heat index back to Celsius: (°F − 32) × 5/9

   $\left(86.5692391\text{\hspace{0.17em}°F}-32\right)\times \frac{5}{9}$$=30.31624394\text{\hspace{0.17em}°C}$

10. Heat index (feels like): 33.2 °C

1. The weather service's formulas use °F, so convert first: °C × 9/5 + 32

   $32\text{\hspace{0.17em}°C}\times \frac{9}{5}+32$$=89.6\text{\hspace{0.17em}°F}$

2. First, make a quick estimate from the air temperature T and the humidity RH. It tells us if the full formula is needed

   $0.5\times \left(89.6+61+1.2\times \left(89.6-68\right)+0.094\times 45\right)$$=90.375\text{\hspace{0.17em}°F}$

3. Average it with the air reading. That's 80 °F or more, so we need the full Rothfusz formula

   $\frac{90.375+89.6}{2}$$=89.9875\text{\hspace{0.17em}°F}$$=\text{≥ 80}$

4. Put the air temperature (in °F) and the humidity (in %) into the Rothfusz formula. Then add up its nine parts

   $\text{−42.379 + 2.04901523T + 10.14333127RH − 0.22475541T·RH − 0.00683783T² − 0.05481717RH² + 0.00122874T²RH + 0.00085282T·RH² − 0.00000199T²RH²}$$=\mathrm{-42.379}+2.04901523\times 89.6+10.14333127\times 45+\mathrm{-0.22475541}\times 89.6\times 45+\mathrm{-0.00683783}\times \mathrm{8,028.16}+\mathrm{-0.05481717}\times \mathrm{2,025}+0.00122874\times \mathrm{8,028.16}\times 45+0.00085282\times 89.6\times \mathrm{2,025}+\mathrm{-0.00000199}\times \mathrm{8,028.16}\times \mathrm{2,025}$$=91.83653846\text{\hspace{0.17em}°F}$

5. Convert the heat index back to Celsius: (°F − 32) × 5/9

   $\left(91.83653846\text{\hspace{0.17em}°F}-32\right)\times \frac{5}{9}$$=33.24252137\text{\hspace{0.17em}°C}$