Bank Shot Calculator & Mini Golf
Bounce a putt off the wall, plus the geometry: a bank shot is never shorter than the direct line, and helps less the bigger the obstacle.
The direct line is always blocked on these holes, so you have to bounce. Aim at the hole's mirror image in a wall and the bounce takes care of itself — "Show a line that works" draws the mirror image it used. Nothing is uploaded.
A bank shot is never shorter than the direct line
To bounce into a hole you aim at its mirror image in the wall, and the two legs of the real path add up to exactly the straight line to that image. So "is a bank ever shorter" becomes "is the mirror image ever closer than the hole" — and with the wall at x = 0 and both points beyond it, |P − T′|² = (px + tx)² + (py − ty)² against |P − T|² = (px − tx)² + (py − ty)². The first is larger whenever px and tx are positive. Strictly longer, always.
| Over 59,967 random placements, all four walls | |
|---|---|
| Times a bank beat the direct line | 0 |
| Typical bank, as a multiple of the direct line | 2.33× |
| The most favourable tenth of placements | 1.167× |
| The shortest bank seen at all | 1.000017× |
Not once. And the bound is exactly one — the shortest bank in the whole sample came to 1.000017 times the direct line, which is the limit approached as the ball creeps onto the wall itself and never crossed. The typical bank is more than twice as long, so it is a real detour rather than a near miss.
So it is for getting round things — and it gets worse as they grow
The only reason to bank is an obstacle. Put a rectangle in the middle of the table, sample ball and hole positions outside it, and ask two things: how often the direct line is blocked, and how often a single bounce gets round it.
| Obstacle | Direct line blocked | One bank rescues it |
|---|---|---|
| 10 × 30 | 37.6% | 72.8% |
| 16 × 40 | 46.5% | 34.4% |
| 24 × 50 | 52.2% | 8.5% |
The two columns move in opposite directions, which is the wrong way round from the intuition. A bigger obstacle blocks more shots and makes banking less likely to help — from 72.8% of blocked shots down to 8.5% — because one bounce cannot get round it either. The bank shot is most useful against the obstacle you were least worried about.
Both tables are frozen, so fresh placements they have never seen are measured at build time as a check: 0 banks shorter than direct out of 7,995, and one bounce rescuing 73.7% of blocked shots past the small obstacle against 6.5% past the large one.
How to use
- The direct line is always blocked, so you have to bounce.
- Aim at the hole’s mirror image in one of the four walls.
- Set the angle with the slider and press Putt.
- Press Show a line that works to see the mirror image it used.
- Press New hole for a fresh layout.
Frequently asked questions
How do you aim a bank shot?
At the mirror image of the hole in the wall you mean to use. The bounce point is wherever that straight line crosses the wall, and the angle in equals the angle out automatically — you never have to work the angle out yourself.
Is a bank shot ever shorter than going direct?
Never, on any table from any position. The two legs of a bank add up to exactly the straight line to the mirrored hole, and the mirror image is always further away than the hole itself. Across 59,967 random placements against all four walls, a bank came out shorter zero times.
How much longer is it?
The typical bank is about 2.3 times the direct line, and even the most favourable tenth of placements is 1.17 times. The shortest bank seen in the whole sample was 1.000017 times — the bound of exactly one, approached as the ball creeps onto the wall and never crossed.
Then why bank at all?
To get round something. A bank is a detour rather than a shortcut, so it only pays when the direct line is blocked — which on the holes here it always is.
Does banking help more against bigger obstacles?
The opposite, which is the surprise. A bigger obstacle blocks more shots but makes a single bounce less likely to help, because one bounce cannot get round it either. One bank rescues 72.8 per cent of blocked shots past a small obstacle and only 8.5 per cent past a large one.
Why does the angle in equal the angle out?
That is what reflection means, and it is why the mirror-image trick works. The test checks it directly: for every bank it measures the angle of approach and the angle of departure and requires them to match.
Does this send anything anywhere?
No. Every hole is laid out and every putt computed in your browser, and nothing is uploaded.
🔒 This tool runs entirely in your browser. Nothing you enter is uploaded, logged, or stored.