# Help on Nozzle Throat Area Calculation

This is the equation of the nozzle throat area This equation is based from a book called HOW to DESIGN, BUILD and TEST SMALL LIQUID-FUEL ROCKET ENGINES

This is the solution The problem is I don’t understand how did they get the answer I put the problem on the online calculators and it gave me 2.53150233845 while the answer should be 0.0444 in² can someone explain to me how did they get the answer 0.0444 in² please The problem is I don’t know how did he get the answer of = 0.0520461 square inches but when I put the problem on the calculator it shows 2.53 can someone tell how to convert 2.53 to 0.0520 square inch or can someone tell me what to do in order to get the answer of 0.0520 square inch

I managed to reproduce your error.

When it says "^1/2" in the equation, you are supposed to take the square root of the quantity in the parentheses. You are not doing this. You are dividing by 2 instead.

0.0906 / 169.34 = 0.000535

365659 / 38.64 = 9463

.000535 * 9463 = 5.063

5.063 / 2 = 2.53

It should be

.000535 * (9463)^(1/2) = 0.052

.000535 * 97.279 = 0.052

The notation that tripped you up deserves a little explanation. The ^ symbol is sometimes used in plain text to indicate exponentiation in environments that don't support superscript, so "x^1/2" just means $$x ^ \frac 1 2$$. Raising to the 1/2 power is the same as taking the square root, so "^1/2" means "square root".