# How to input pi

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Anthony
on 20 Sep 2016

Commented: Walter Roberson
on 27 Jul 2024 at 16:58

How can i enter pi into an equation on matlab?

##### 2 Comments

Vignesh Shetty
on 6 Apr 2020

Hi Anthony!

Its very easy to get the value of π. As π is a floating point number declare a long variable then assign 'pi' to that long variable you will get the value.

Eg:-

format long

p=pi

Walter Roberson
on 16 Dec 2022

### Accepted Answer

Geoff Hayes
on 20 Sep 2016

Edited: MathWorks Support Team
on 28 Nov 2018

Anthony - use pi which returns the floating-point number nearest the value of π. So in your code, you could do something like

sin(pi)

### More Answers (5)

Essam Aljahmi
on 31 May 2018

Edited: Walter Roberson
on 31 May 2018

28t2e−0.3466tcos(0.6πt+π3)ua(t).

##### 5 Comments

Image Analyst
on 20 Oct 2018

Attached is code to compute Ramanujan's formula for pi, voted the ugliest formula of all time.

.

Actually I think it's amazing that something analytical that complicated and with a variety of operations (addition, division, multiplication, factorial, square root, exponentiation, and summation) could create something as "simple" as pi.

Unfortunately it seems to get to within MATLAB's precision after just one iteration - I'd have like to see how it converges as afunction of iteration (summation term). (Hint: help would be appreciated.)

John D'Errico
on 28 Nov 2018

Edited: John D'Errico
on 28 Nov 2018

As I recall, these approximations tend to give a roughly fixed number of digits per term. I'll do it using HPF, but syms would also work.

DefaultNumberOfDigits 500

n = 10;

piterms = zeros(n+1,1,'hpf');

f = sqrt(hpf(2))*2/9801*hpf(factorial(0));

piterms(1) = f*1103;

hpf396 = hpf(396)^4;

for k = 1:n

hpfk = hpf(k);

f = f*(4*hpfk-3)*(4*hpfk-2)*(4*hpfk-1)*4/(hpfk^3)/hpf396;

piterms(k+1) = f*(1103 + 26390*hpfk);

end

piapprox = 1./cumsum(piterms);

pierror = double(hpf('pi') - piapprox))

pierror =

-7.6424e-08

-6.3954e-16

-5.6824e-24

-5.2389e-32

-4.9442e-40

-4.741e-48

-4.5989e-56

-4.5e-64

-4.4333e-72

-4.3915e-80

-4.3696e-88

So roughly 8 digits per term in this series. Resetting the default number of digits to used to 1000, then n=125, so a total of 126 terms in the series, we can pretty quickly get a 1000 digit approximation to pi:

pierror = hpf('pi') - piapprox(end + [-3:0])

pierror =

HPF array of size: 4 1

|1,1| -1.2060069282720814803655e-982

|2,1| -1.25042729756426e-990

|3,1| -1.296534e-998

|4,1| -8.e-1004

So as you see, it generates a very reliable 8 digits per term in the sum.

piapprox(end)

ans =

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199

hpf('pi')

ans =

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199

I also ran it for 100000 digits, so 12500 terms. It took a little more time, but was entirely possible to compute. I don't recall which similar approximation I used some time ago, but I once used it to compute 1 million or so digits of pi in HPF. HPF currently stores a half million digits as I recall.

As far as understanding how to derive that series, I would leave that to Ramanujan, and only hope he is listening on on this.

Walter Roberson
on 20 Oct 2018

If you are constructing an equation using the symbolic toolbox use sym('pi')

##### 3 Comments

Steven Lord
on 22 Oct 2021

That's correct. There are four different conversion techniques the sym function uses to determine how to convert a number into a symbolic expression. The default is the 'r' flag which as the documentation states "converts floating-point numbers obtained by evaluating expressions of the form p/q, p*pi/q, sqrt(p), 2^q, and 10^q (for modest sized integers p and q) to the corresponding symbolic form."

The value returned by the pi function is "close enough" to p*pi/q (with p and q both equal to 1) for that conversion technique to recognize it as π. If you wanted the numeric value of the symbolic π to some number of decimal places use vpa.

p = sym(pi)

vpa(p, 30)

Dmitry Volkov
on 16 Dec 2022

Easy way:

format long

p = pi

##### 1 Comment

Walter Roberson
on 16 Dec 2022

Meghpara
on 27 Jul 2024 at 6:11

it is easy to ge pi

in p=PI.

##### 1 Comment

Walter Roberson
on 27 Jul 2024 at 16:58

p=PI

If you meant

p=pi

then @Vignesh Shetty suggested exactly that https://www.mathworks.com/matlabcentral/answers/303687-how-to-input-pi#comment_822235 several years ago, which in turn is functionally equivalent to what @Geoff Hayes suggested in 2016 https://www.mathworks.com/matlabcentral/answers/303687-how-to-input-pi#answer_235320

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