I would like to draw circles and ellipses more accurately without relying on a compass (or spinning my paper around). This seems like a simple google-searchable question, but most of the results are flooded with click-bait "amazing circle drawing trick!" results.
How do you draw a near-perfect circle without using or mimicking a compass?
I do not know whether you see a pin and a bit of string as a compass mimicking method, it is likely a very old alternative.
You can do elipses by using two pins and a bit of string.
Or you an use circular items and draw a line around it, just like you draw a straight line along a ruler.
There are special tools which have a series of circular holes to allow to make quickly draw several sizes of circles, if you search on -circle template ruler- you will see several different options. (Here is a link to a commercial site which shows one.)
The best method without any tools is training.
The more you do it, the better you will become.
Sit with a piece of paper in front of you and draw as many circles as you can, look critical and try to improve.
There are several methods of drawing which may work for you.
One is one flowing line, no options to improve once started but a very strong result when done right.
A second one is to build up the circle from tiny fragments. Like for a circle with 10 cm/4" diameter you draw little lines about 1 cm/ 1/2" long and overlap them at least one third, maybe two thirds. With this method you can stop and consider, re-adjust and change the shape while working on it. Even in the best outcome it will not show as strong as the single line approach but I find it an easier way to get near the perfect circle. (I never really get it right out of hand, I prefer the computer to make perfect circles for me.)
Maybe it will help you to have a perfect circle of about the right size near while training yourself to draw one. This can be any simple item which is circular. Samples include coins, saucers, tops or bottoms of glasses or even the rings left by a wet glas and so on.
An other training exercise might be that you use a circle made by one of the mechanical ways (compass tool or drawn around an object, or again the ring left by a glass) and draw your training circle around or inside (or both and several on each 'side'.)
Some people will be able to draw almost perfect circles by hand, without much training, others will never learn it. You have to try to find out how good you are.
1.First, draw a rectangle. In which you imagine your circle or ellipse to be fitting in.
2.Next, mark the mid-points of all four sides.
3.Keeping in mind that the sides are tangents and mid-points are where tangents meet the curve start to draw curve near the four midpints.
4.You'll see a rough ellipse emerging. It should be easy hereafter.
Later on, when you've enough practice you can do steps 1, 2 and 3 in your head.
Holding your pencil firmly and keeping your hand position the same, use the bone of your pinky as pivot and turn the page.
There are a lot of household items that are circular. Consider the coins in your pocket, the cans on your shelf, the plates in the cupboard, any and all of these can be set onto your paper or canvas and traced around the edges to create circles.
A wooden ruler can provide accurate diameters by using a push pin set at a desired distance and placing your pencil point on the outside edge and in line with your pin. Much like the string but more manageable.
Ellipses and ovals are more challenging. There are few if any lying around the house to trace, but there are multitudes on the internet you can call on, print and trace or transfer with carbon paper or graphite.
Whether you want an ellipse to capture an image from life or an oval to make a decorative form increases or decreases the complexity. Using downloaded oval prints will make a flying saucer unreal, but hoop earrings in a portrait will pass as will a wall paper design. The viewer wants to believe the saucer picture and will detect a problem with perspective, whereas the earrings in a drawing are easily overlooked and the ovals on wallpaper design are subject to the artist's discretion.
A circle on edge is a line and the higher the line is lifted the more elliptical the circle appears. To prove this, draw a diameter line on a paper plate. Then place the plate flat on a table, diameter line down. With you looking directly at it's edge, lift the side closest to you and capture the image in your mind's eye. At no point can I see a perfect ellipse as perspective brings the diameter line closer to you until the plate is perpendicular and becomes circular. As you continue to flip the plate on edge, the diameter line will now move away from your eye and yet you still have an ellipse, but not an oval
My point is this, unless you want a mathematically perfect oval your problems are multitude, but not impassable. Still,"There ain't no easy way out!"
Some options:
Mohits answer above with the square is a good way to start but here's how I learned to draw circles and ovals (ellipses) freehand.
First, learn to draw circles and ovals with your shoulder and elbow. Your whole forearm should move when you draw a circle or oval. Except for very small circles, you will never be able to draw good circles with just your fingers and wrist.
Next, draw squares of various sizes and draw circles that fit exactly inside those squares. Check your work by folding the paper in half through the middle of the circle and holding the folded paper up to the light. The lines of both sides should line up exactly.
Finally, fill a page with circles of various sizes every day until you master the skill. This skill takes practice.
When you've mastered circles, practice ovals. The technique is the same as circles except that you will be folding your paper in half along the long side and then the short side of the oval.
When you start drawing circles and ovals in perspective, first draw a square in perspective and then use Mohit's method to draw the circle within the square.
Here are a couple of videos showing options for using only your hand, stylus and rotating a sheet of paper, plus some other options using household items like paper clips.
If size allows, just use a circle stencil/template.
