F-distribution

The F-distribution curve

a₁ = 0.196854
a₂ = 0.115194
a₃ = 0.000344
a₄ = 0.019527

d₁ = degrees of freedom in numerator
d₂ = degrees of freedom in denominator

clc; clear 

% Asks the user for the relevant input
f = input ('Enter F-value: ');
d1 = input('Enter degrees of freedom in numerator: ');
d2 = input('Enter degrees of freedom in denominator: '); 

x = 1;
% Computes using inverse for small F-values
if f < 1
    s = d2;
    t = d1;
    z = 1/f;
else
    s = d1;
    t = d2;
    z = f;
end
j = 2/(9*s);
k = 2/(9*t); 

% Uses approximation formulas
y = abs((1 - k)*z^(1/3) - 1 + j)/sqrt(k*z^(2/3) + j);
if t < 4
    y = y*(1 + 0.08*y^4/t^3);
end 

a1 = 0.196854;
a2 = 0.115194;
a3 = 0.000344;
a4 = 0.019527;
x = 0.5/(1 + y*(a1 + y*(a2 + y*(a3 + y*a4))))^4;
x = floor(x*10000 + 0.5)/10000; 

% Adjusts if inverse was computed
if f < 1
    x = 1 - x;
end 

% Displays results
str1 = ['Percentile = ' num2str(1-x)];
str2 = ['Tail end value = ' num2str(x)];
disp(str1)
disp(str2)

What is the percentile on an F-distribution curve when the F-value is 0.474 and the degrees of freedom are 1 and 18?

We run the code above and enter the data: 

Enter F-value: .474
Enter degrees of freedom in numerator: 1
Enter degrees of freedom in denominator: 18

What is the percentile the F-value is 23.7 and the degrees of freedom are 3 and 6?

We run the code above and enter the data: 

Enter F-value: 23.7
Enter degrees of freedom in numerator: 3
Enter degrees of freedom in denominator: 6