← practice

Why you can't draw a straight line

The wobble is mechanical, and so is the fix.

A line drawn from the wrist is drawn by a hinge sitting a hand's width behind the nib, and a hinge sweeps an arc. Pull six lines that way and they do not scatter at random: they all bow the same direction, because they were all made by the same joint turning the same way. That is the most useful fact in this chapter. What people call an unsteady hand is usually not unsteady at all — it is a consistent curve produced by the wrong pivot, and a consistent error is a fixable one.

Three changes follow from it, and they are the whole of line practice. Draw from the shoulder, so the arc is long enough to read as straight across a page. Commit to the stroke instead of steering it, because steering is a stream of small corrections and a correction is what makes a line look shaky. Look at where the line is going instead of at the nib, for the same reason you look at the corner rather than the bonnet when you are driving.

Below, each of those is explained and then measured. The site has ten drills for this chapter, and because the scoring runs here in the page, this guide can say what "too curved" costs in pixels and degrees rather than asking you to take its word for it. Every figure quoted comes out of the drill's own js/game.js.

Draw from the shoulder, not the wrist

There are four hinges available and they draw four different lengths of line. Fingers write; they are for lettering and for marks the size of a letter. The wrist hatches and does short curves. The elbow carries a line across most of a sketchbook page. The shoulder, with the elbow locked and the whole forearm swinging, carries a line across anything larger — and it is the only hinge that will take a long curve in one go instead of building it out of segments.

Beginners default to the wrist because handwriting trained them to, and handwriting is the one graphic skill nobody has to learn twice. The cost is invisible until somebody measures it, which is exactly what the straight-line drill does: six pulls between two dots, then a sentence at the end of the round about the shape your six lines had in common.

What Steady Lines measuresThe RMS perpendicular drift of your stroke away from the straight path between the dots. Under max(0.4% × |AB|, 3px) it is a flat 100; the score reaches zero at ease × max(5.5% × |AB|, 16px). Note what the 3px floor does: on any pull shorter than 750px the free zone is a flat 3px no matter how long the line is, so a longer stroke buys you a wider zero point but never an easier perfect. A further 20 points are available to lose on the combined miss at the two ends, once it passes ease × 24px.

The lean it names out loudAt the end of a round the drill takes each stroke's mean signed offset from the ideal path as a fraction of the line's length. If more than 0.006 of them lean the same way on four of the six strokes, it prints "every line arcs the same way — that is the wrist pivoting". On a 300px pull, 0.006 is 1.8px of average lean. That is a bow you cannot see and the drill can, which is the only reason the sentence is worth anything.

Why a mouse is allowed twice the wobble

Every motor tolerance on this site is multiplied by an ease factor before it is applied: 1.0 for a pen or stylus, 1.5 for a finger, 2.0 for a mouse or trackpad. That is not a courtesy. It is the same fact about pivots, stated from the other side. A mouse is moved by a hand rocking on the heel of the palm, and a wrist rocking through a short arc physically cannot creep along a curve the way a nib on paper can — the error it makes is a different error, of a different size, so grading it against the pen's number would only tell trackpad owners they are bad at drawing.

The consequence is worth knowing before you compare anything: a best score set with a pen tablet and one set with a trackpad are two different measurements. Each drill prints which hardware it is scoring for. Switch, and expect the old number to be sitting under a differently sized allowance.

Ghost it, then commit

Ghosting is the habit that separates a drawn line from a traced one. You rehearse the stroke in the air above the paper two or three times at the speed you intend to draw it, watching the end point rather than the pen, and then you put the pen down and repeat the movement once without slowing to check. The rehearsal is where the aiming happens. The stroke itself is not aimed at all — it is executed, and the reason it comes out straight is that the arm has already done it three times.

The hard part is not learning that. It is believing it, because a fast line is wrong in an obvious way and a slow line is wrong in a way you can pretend not to see. The superimposed-lines warm-up is the exercise that makes the trade legible: one faint guide, drawn four times from the same dot, each repeat in darker ink so the fan your own hand made is sitting there to look at. Crucially, you are not scored against the guide. You are scored against the average of your own four attempts.

What Superimposed Lines measures(55 × fray + 30 × commitment) × cover + 15 × start. Fraying is the RMS perpendicular spread of the four repeats about their own mean path, as a fraction of the line's length: the first 0.5% is free and it reaches zero at 6%, eased — so on a 400px guide, a fan spread of 2px still scores full marks and 24px scores none with a pen, 48px with a trackpad. Commitment is the RMS turning angle along the stroke with the mean turn subtracted, so an intended curve costs nothing and only the corrections show: free below 0.012 radians and zero at 0.095, eased like everything motor here — about 5.4° of scatter between one step of the stroke and the next, on a pen.

Four confident copies of a slightly wrong line beat four timid different ones, and the arithmetic says so: fraying is 55 points and hugging the guide is worth nothing at all. If your fan is tight and your score is still middling, the missing points are commitment, and the fix is counter-intuitive — go faster and stop correcting. Steady Lines reads the same thing as a coaching note it deliberately keeps out of the score: it takes the coefficient of variation of your stroke's speed and calls anything at or under 0.45 one confident pull, anything at or over 1.6 stop-start hesitation. It is printed and never charged for, because a slow line that lands is still a line that landed.

The one drill where steering is the point

Committing is not the same as not looking. Steady Tunnel is the deliberate counter-case: a corridor that winds across the sheet and narrows as it goes, which you have to steer down while the room for error closes. It rewards the habit the other line drills cannot teach — reading the path ahead of your own nib. Staying between the walls is worth 0.75 of the score and running down the middle of them 0.25, so touching a wall costs three times what drifting off-centre does. The last tunnel's exit half-width is 1.9% of the canvas height and never under 12px before easing, and on any ordinary screen that floor is what bites: the gap you are steering through at the flag is 24px wide with a pen and 48px with a trackpad. Easing widens the corridor, but it also widens the wiggle, so an easier lane still has to be steered rather than crossed.

A warm-up is range of motion, not accuracy

Ten minutes of careful hatching is not a warm-up. What warming up does is give the shoulder and elbow their full travel back before you ask them for anything precise, and precision is the thing you specifically do not want during it. Loose overlapping circles, long diagonal sweeps corner to corner, big lazy figure eights — drawn fast, drawn ugly, drawn much larger than the drawing you are about to make.

That is a hard thing to make yourself do when a number is watching, so the warm-up drill is scored to reward the right thing: 60 of its 100 points are for how much ink you moved and only 40 for a loose shape check. The distance target is four diagonals of the box, whatever size the box came out on your screen, which is about 25 seconds of unhurried scribbling. The shape half is then scaled by how far you got, all the way up to a quarter of that target, so a hand trembling in one spot collects next to nothing for accidentally drawing something round.

How loose is loose enoughDiagonal sweeps hold full marks while their directions agree within 22° on a pen — 44° on a mouse — and fall to zero at twice that, with a sweep and its return counted as one axis rather than two. Loose circles count as round if the loop's 5th-to-95th-percentile radius band stays inside 0.35 of its own mean radius on a pen, 0.70 on a mouse — at 0.35 a 1.5:1 oval is thrown out, at 0.70 more or less anything loop-shaped counts. Nothing here is asking for a good drawing.

The drill also converts what you drew into distance, at roughly 3780px to the metre — 96 CSS pixels being about an inch — and tells you how far your hand travelled. It is a small thing, but it reframes the exercise correctly: a warm-up is a quantity of movement, and the only failure available is not moving.

Ellipses are circles seen at an angle

An ellipse is not a shape to memorise. It is a circle rotated away from you, and the amount it has rotated is the only thing that changes: tilt a circle by an angle of acos(minor ÷ major) and its outline is that ellipse. Artists call how far it has turned the ellipse's degree. Ellipse Orbit shows this literally rather than asserting it — after each attempt a real circle rotates in 3D until its projection lands on the target you were given.

Knowing that changes what you are aiming at. A wheel drawn on a car is not a squashed oval you invented; it is a circle sitting in a plane, and the plane decides the squash. That is also why this chapter and the perspective chapter overlap — once you can draw an ellipse, laying it into a plane you have constructed is the next step, and it belongs over there.

What Ellipse Orbit measuresMean distance, in pixels, from every resampled point of your loop to the true curve. The score reaches zero at max(18% × the box's mean radius, 14px) times the hardware ease, and the first 9% of that band is free — so on a box of mean radius 100px a pen has to hold the loop inside an average 1.6px of the true curve for a flat 100 and scores nothing at 18px, while a trackpad gets 3.2px and 36px. Two more gates: under 75% of the way round nothing is scored at all (the loop simply waits for you), and an unclosed loop whose ends miss each other by more than 12% of the perimeter costs up to 10 points, in full by 24%.

Accuracy is only half of it, though, and it is the half most people practise. The other half is repeatability, which is what "draw through your ellipses" has always meant: go round two or three times without stopping, so the second and third laps land on the first. Draw Through is the drill that actually checks whether they did. It unwraps your stroke into an angle around the centre, cuts it into laps, reads every lap at the same 64 fixed directions, and compares them with each other.

What Draw Through measures75 points for how tightly the three laps stack and only 25 for drawing the ellipse that was asked for. Agreement is the mean spread of those 64 radii about the laps' own average, reaching zero at 13px × ease × a weak size factor clamped between 0.85 and 1.25. It also tracks drift — the last lap minus the first — and when the mean lean clears a tenth of the tolerance on at least 60% of the round's loops, it names the habit: "every loop grew as it went round". That outward spiral is the standard beginner ellipse, and it is the reason the third lap is worth drawing.

What is the eye's fault, and what is the hand's

Some line errors are motor and some are judgement, and it is worth being able to tell which one you are having, because the fixes have nothing to do with each other. A motor error gets better with repetition and warming up. A judgement error gets better by measuring — by holding your pencil up, comparing, and marking before you commit.

Angle Snap isolates the judgement half. It asks for a stroke at a named angle from a reference line and fits the direction across every sample of your pull by least squares, which means smoothness drops out of the maths entirely: a shaky mouse line and a ruler-straight tablet line with the same principal axis score identically. The design decision underneath is the one worth carrying to any drill on this site — the hardware allowance is spent on what the hardware does and never on what the eye does.

What Angle Snap eases, and what it does notPast the free zone, the score falls linearly to zero at 25° of angular error, and that 25° is not eased for hardware, because it grades a judgement and no pointer judges better than another. The free zone is eased, because it exists to absorb pointing jitter: min(8°, 2° + atan(ease × 2.5px ÷ pull length)). Jitter of 2.5px is 3.6° across a 40px pull and 1.2° across a 120px one, which is why the zone shrinks as you pull further — and why a short stroke is a worse way to judge an angle than a long one.

Mirror Mirror puts the same idea to work on a shape. Half a figure is drawn against a mirror line and you freehand the other half. Copying the given outline stroke for stroke is the slow way to be wrong; the method that works is to pick three or four heights, read how far the drawn half sits from the axis at each of them, mark that distance out on your side, and only then join the marks. The scoring band reflects the split explicitly: the hardware allowance is added to the tolerance rather than compared with it — +16px for a mouse, +8px for a finger, on top of max(8% × the figure's height, 16px) — because judging where the mirror is costs the same on every device, and only landing the mark you judged is a pixel count.

Spacing and weight are line skills too

Most of the marks in a finished drawing are not single confident lines. They are groups: hatching, contour bands, a row of pickets, the repeated ticks along an axis. What makes a group read well is almost never the straightness of its members — it is the evenness of the gaps between them, which is a placement problem wearing a line problem's coat.

Even Spacing is that skill on its own. Cross a baseline with three evenly spaced ticks, then five, then fill two boxes with parallel strokes. Its tick tolerance is generous in a way that is itself instructive: the free zone is max(4% of one gap, 3px) and the score runs out at max(40% of a gap, ease × 16px). On a 600px baseline split into four, that is 6px for a perfect and 60px before you score nothing — you are allowed to be almost half a gap out. Dividing by eye is harder than it looks, and the band is set where honest attempts land.

The fills are weighted the other way and it is the most opinionated number in the chapter: 65% of a fill's score is rhythm — how far the gaps between your strokes wander from their own average, against max(42% of the mean gap, ease × 5px) — and only 35% is parallelism, which runs out at ease × 14° of angular spread. Hatching that is perfectly parallel and unevenly spaced looks worse than the reverse, and the weights say so. (If you are hatching to build tone rather than texture, the value chapter is where that continues.)

Then there is weight itself. A drawing made entirely of one unvarying line thickness reads as flat and traced, and Line Weight exists to charge for it. You redraw a target stroke's thick-and-thin along a dashed guide; both width profiles are sampled at 64 positions, normalised, and compared by RMS difference.

Why a flat stroke scores zero, by measurementThe RMS at which the score dies is 0.34 on a pen. That constant is not taste — a stroke of one constant weight measures about 0.34 RMS against these targets and random noise about 0.42, so the zero point is set precisely where the mistake the drill exists to correct lands. It is eased for other hardware but capped at 0.50, so "one flat weight fails" stays true in every input mode, and a stroke using less than 20% of the available width range takes a further ×0.8.

Two more sit at the edges of this chapter. A freehand circle is the purest test of the shoulder pivot there is — the score is RMS radial deviation from a least-squares circle fitted to your own stroke, divided by that circle's radius, so a small circle and a big one are judged identically. And the line that wraps a form takes straight-line control into three dimensions, which is a perspective problem rather than a hand one.

What a browser drill cannot teach you

It is worth being clear about the boundary, because a page that only lists its own strengths is not much use to a teacher deciding whether to send it.

And one thing about the scores themselves: they are compared with your own past rounds and nothing else. No model marks anything on this site. Six of this chapter's drills are pure closed-form geometry and four compare your marks against a reference the drill computed; none of them uses a curated answer key, and every number above can be checked by opening the file it came from.

How to practise this week

Ten to twelve minutes a day, and the order matters more than the total.

  1. Every day, two minutes: the warm-up sets, drawn deliberately too big and too fast. Ignore the shape half of the score entirely for the first week; watch only that you are filling the ring.
  2. Monday and Thursday: superimposed lines. Do not read the total. Read the verdict sentence — if it says the lines wobble, your problem is commitment, and the instruction is to pull faster and never correct mid-stroke.
  3. Tuesday and Friday: straight-line practice. The number to watch is not the score, it is whether the round-end sentence names a lean. That sentence appearing means four of your six lines bowed the same way, which is a pivot you can change today.
  4. Wednesday: three laps of an ellipse. If the drill tells you every loop grew as it went round, slow the first lap and let the second and third ride on it rather than outside it.
  5. Saturday: whichever of judging angles, dividing by eye or weight control came back lowest. These three are judgement, so they improve in steps rather than smoothly.

On reading the numbers: a five-point week is noise. The signal to watch for is categorical — the day the lean sentence stops appearing at the end of a Steady Lines round, or the day Draw Through stops calling your loops a spiral. Those are statements about a habit rather than a measurement of one attempt, and they are what actually changed.

Next: perspective — where these lines start having to agree with each other · observation — judging what is in front of you · all six practice guides · the catalogue, 43 drills