Dear John,
PERCENTAGE OVERALL SLOPE. The first way to judge the tilt of a green is to use your putter at the lowest part of the green: set the putter sole on the green and sight however high up the vertical shaft is needed to look level across to the highest part of the green. If you look across the top of the handle of a 35-inch putter, the elevation change from low to high is 35 inches (about 3 feet). That's half of what you need (the "rise"). You also need the "run" or horizontal distance from the low point (where the putter is located) to the high point of the far fringe of the green. If this distance is, say 75 feet, then you have Slope = Rise / Run. Because you are sighting the WHOLE green in general, this method gauges the slope in general, not the specific slope at your ball's location towards the hole.
This gives you the Slope in terms of percentage. A 3% slope rises 3 feet for every 100 feet of run. In the example of 3 feet of rise for 75 feet of run, the Slope = 3/75, which is 4% slope (fairly steep, but not the steepest). Another example would be to sight across the putter shaft half way up (1.5 feet) to a high spot 50 feet away: rise = 1.5 feet, run = 50 feet. Slope = 1.5/50, or 3% slope.
FLAGSTICK METHOD. From the fairway, you can often use the flagstick to estimate overall green slope in percent, especially when the flag is up front and the green slopes towards the fairway. Look up the flagstick 1 foot high and sight behind the flagstick at that height until you hit the green surface. The proportion of rise to run is the slope in percent. For example, if you sight behind the flag and this line hits the surface 30 feet behind the pin, this is about 3% slope (1/30). A run behind the pin of 40 feet corresponds to a 2.5% slope.
PERCENTAGE SPECIFIC PUTT SLOPE. An alternative way to gauge slope with your putter is to use inches instead of feet. This will allow you to focus on the slope between the ball and the hole. Wherever your ball is located (if lowest -- uphill putt) or wherever the hole is located (if lowest -- downhill putt), hold the shaft vertical with the sole near the low point and estimate the rise in inches up the shaft when sighting level across to the high spot, then estimate the run in inches, and divide the Rise by the Run for percent slope.
Because this is a bit tricky (to get low enough to sight, and to do the math), here is a slightly easier method. Select a spot along the same sight line from low to high that is 100 inches away from the low point (100 inches is 8 feet and 4 inches, or about 3 paces). Sighting the elevation rise from low to this spot 3 steps or 100 inches away then eliminates the need to do the math. If the Rise is 3 inches, then the Slope is 3% -- simple. Whatever the Rise to this 100-inches-away (or 3 steps away) spot, that is also the Slope (no math).
You can use this trick also when sighting the "general" slope using feet: just select a high spot that is 100 feet away (about 30-35 paces), and whatever elevation Rise you sight is also the Slope. And since 100 feet is typically a bit too far for most greens, use one-half or on-fourth of that by sighting a high spot that is 50 feet, or 25 feet, away, and then multiply the elevation Rise in feet along the shaft by 2 (for 50 feet) or by 4 (for 25 feet) to get percent slope. A green that rises 1 foot to a spot 25 feet away (about 8 steps) is a 4% slope.
DEGREES OF SLOPE. The second way is to estimate degrees of slope. A 3-degree slope is NOT the same as a 3-percent slope. The degrees of slope are trickier and less useful. Surveyors and grading contractors use percentage slope, not degrees. But if you want to know degrees, you have to think in terms of a 45-degree slope as being the same as a 100-percent slope. When the surface is tilted 45 degrees, then it rises 100 feet for every 100 feet of run. If the slope rises 1 foot for 100 feet of run, the trigonometry is that the "angle" of slope at the ball uphill to the target is ARCTANGENT(1/100), = 0.573 degrees. So, one percent of slope is the same as 0.573 degrees of slope, and one degree of slope corresponds to 1.75% of slope. A 2% slope is then 2 x 0.573 degrees, or 1.164 degrees of slope. A 2-degree slope is a 3.6% slope. This relationship graduates from 1%=0.573 degrees when the slope is mildest up to 1%=0.45 degrees when the slope nears 100%, but in the normal range of green slopes, 1%=0.57 degrees is a good correlation. Even at 50% slope, the correlaton is still 1%=0.53 degrees.
Because math is too tricky on the fly, here's an easier way. Stand at the lowest part of the green. Look to a spot that is the same distance away along the ground horizontally as your eyes or forehead is high (assumed to be 70 inches high, roughly, for easy math). So, every 7 inches up your leg for a 6-foot male is 1/10th of the way up to the eyes. If the spot 70 inches off rises up the leg 7 inches, then that is 1/10th of the way to 100%, and 10% then corresponds to 5.7 degrees of slope. That's a LOT. A more normal slope would have the spot 70 inches off rise up your leg only one-third or one-fourth that far (3% or 2.5% slope). Generally speaking, if you look 2 steps away and estimate the rise, a 3% slope (2.7 degrees) comes up your leg about ankle high (2.5 inches), whereas a 1% slope (0.57 degrees) comes up only about toe-high or 0.7 inches.
BALL SLOPE: Another way is to start with the diameter of a golf ball (1.68 inches). If you lined up 100 golf balls, that would be 168 inches, which happens to be 14 feet exactly (odd, but true -- 12x14=168). So, 14 feet away for a high spot (about 5 steps) yields the result that each "ball" of rise is equivalent to 1 percent of slope or 0.57 degrees of slope. This allows you to look 5 steps from your ball, estimate the number of "ball" of elevation rise (or drop), and that is your percent slope.
HAND SOLPE: Another way is too look at the slope from the side. Position yourself off to the side of the ball-hole line, and estimate what the slope would look like if the hole were elevated above the ball height the same height as the distance of the putt (a 45-degree or 100% slope). Then guess what fraction the actual slope is of that maximum slope. If the actual slope appears to be about 1/10th, then the slope 10%, or 10x0.57 degrees (5.7 degrees of slope). If the actual slope is 1/20th of the 100% slope, then the slope is 5%, or 5x0.57 degrees (2.85 degrees of slope). You can use your hand starting at a 45-degree angle, and then reduce it to level by halves (22.5 degrees / 39.5%, 11.25 degrees / 19.7%, 5.625 degrees / 9.9%, 2.8125 degrees / 4.9%) to get down to the real world of slopes. Roughly speaking, it takes at least 4 reductions of 45 degrees by halves to get to typical green slopes, so this measure is not very accurate (how do you discriminate between the 4th and 5th halves, since they are already pretty small angles?)
As you will quickly realize, getting precision in these very fine estimates is a real challenge. Basically, because the percent slope is a more BLUNT measurement (over twice as blunt), it is a whole lot easier than a degree estimate.
HUMAN INCLINEOMETER. Because all of this is pretty rough, a simple way to gauge slope is to make yourself into an inclineometer. An inclineometer is a base that matches the slope plus a tower from which hangs a plumb line (or a bubble level in a horizontal tube of glass). Our model is the plumb line sort. As the slope increases, the plumb line swings farther and farther out from its starting position (level surface) directly below the top of the tower. A golfer's feet are the base, his shoulders are the top of the tower, and his putter suspended in gravity is his plumb line. So stand on either side of your ball, flat footed so that the vertical axis of your body is perpendicular to whatever slope you stand on. With your shoulders in line with the ball vertically, let your arms hang holding the putter. The arms will swing away from you as you face / tilt downhill. The sweetspot of the putter will stop above the ground a certain number of inches out past the ball. The ANGLE of tilt of this slope (in degrees) is from the trigonometry: The horizontal "slippage" of the sweetspot past the ball is distance A, and the height of your shoulders is distance B. When the degrees of slope is D, the Tangent(D) = A/B. So, to find D, take the ARCTANGENT of A/B. For example, when a golfer is 6 feet tall (72 inches), his shoulders at address posture are about 4.5 feet (54 inches) off the ground. For every 1 inch the sweetspot swings out past the ball, this is the same as ARCTANGENT(1/54) = 1.06 degrees. In simple terms, every 1 inch the putter swings past the ball is about 1 degree of slope and 1.75% of slope. (A "radian" is 180 degrees / 2 * pi, or 57.3 degrees. ARCTANGENT(1/57.3) = 1 degree, so 57.3 inches high is really the "magic" number for 1 inch of swing.) So position your shoulders over the ball, aim the putter at the ball standing flat-footed, then relax the arms and see how far out past the ball the putter swings. Every inch of swing is 1 degree or 1.75% of slope.
Because of these different methods, here is a chart of RISE over RUN that collects them all together (roughly):
1% = 12 inches or 1/3rd of putter shaft rise over 100 feet / 33 steps run
1% = 6 inches or 1/6th of putter shaft rise over 50 feet / 17 steps run
1% = 3 inches or 1/12th of putter shaft rise over 25 feet / 8 steps run
1% = 1 inch rise over 8'4" feet / 100 inches / 3 steps run
1% = 0.7 inch or top of toe rise over 70 inches / 5'10" / 2 steps run
1% = 1 ball rise over 100 balls / 168 inches / 14 feet / 5 steps run
1% = over 4 halvings of 45 degree hand angle to 5% slope and under
1 deg. = 21 inches rise over 100 feet / 1200 inches / 33 steps run
1 deg. = 11.5 inches rise over 50 feet / 600 inches / 17 steps run
1 deg. = 5.75 inches rise over 25 feet / 300 inches / 8 steps run
1 deg. = 1 inch rise over 4.8 feet / 57.3 inches / 2 steps run
1 deg. = 1 inch swing from under 4'9.7" feet / 57.3 inches tower (shoulders)
Conversion factors:
1 % slope = 0.57 degree slope
1 degree slope = 1.75 % slope
I like the HUMAN INCLINEOMETER approach best. You can only ballpark the slope anyway, and this is a good read on where you stand. Assuming the rest of the way to the hole is the same general slope, this method works pretty good. If not, you have to estimate the difference in height between ball and hole.
Cheers!
Geoff Mangum
Putting Theorist and Instructor
Geoff Mangum's PuttingZone
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