What is Tau?

Tau is two Pi.
That is,  τ  =  2 π
 Numerically, it is 6.283…

Why?

Short answer:
To make radians easier.

We think in complete circles.

We see the wheel as one circle
instead of two semi-circles.

When the wheel turns, we think in revolutions.
We never ask how many half-revolutions it does.

In radians,
1 revolution equates to 2 π.

Or 1 π equates to ½ revolution.

This forces us to think in half-revolution.
So ¼ revolution is ½ π radians, or ½ half-revolution.

(It doesn’t help if you speak English.
π sounds like ‘pie’, which is a full circle.)

π makes radians awkward.

With

τ = 2 π

The math is simple

1 τ  radians  =  1 revolution

As trigonometry is actually based on radians,
τ makes it more intuitive. Here is another reason why.

How?

We will work in radians.
Click DEG to switch to RAD.

You can insert  τ  by pressing ⌥T,
but the magic begins when you make τ as the default:

Click and hold  π , then choose τ from the menu.

Let’s get started.

See better with Tau

Making sense of radians is hard.

Magic Number’s fraction has a nice option.

It let’s you see radians as a fraction of τ.

You can also see decimal radians with τ.

Tau as an angle

This is subtle but nice.
It involves trigonometric function and division.

Normal case:

When you enter
sin 7 / 12

You get:

Magic Number assumes you want sin( 7 ) / 12

Special case:

Enter
sin τ / 12

You get:

Magic Number sees τ/12 as an angle,
thus it assumes sin( τ/12 ).

(For normal division, enter ‘sin τ / / 12’)