Ballistics reference
Cosine Angle Chart
Quick answer
At a 30 degree shooting angle the cosine is 0.866, so a 500 yard slant range shot behaves like a 433 yard shot for gravity's purposes. At 45 degrees the same 500 yard slant range shrinks to 353.6 horizontal yards. Dialing the slant range instead of the horizontal equivalent is why steep uphill and downhill shots go high.
Gravity pulls a bullet down, not along the line of the barrel, so what actually matters for drop is the horizontal distance to the target, not the slant distance a rangefinder reads on an incline. This is the rifleman's rule, and the horizontal component of any slant range is exact trigonometry: horizontal distance equals slant distance multiplied by the cosine of the angle from level.
A shot taken uphill or downhill at a steep angle covers less horizontal ground than its slant range suggests, so a correction dialed for the full slant range sends the bullet high. Cosine is always a positive value regardless of whether the angle is up or down, which is the reason the same correction applies to both.
The table below is exact arithmetic. Treating the result as a level shot at the horizontal distance is the part that is an approximation, one that holds up well inside ordinary hunting angles and distances and grows increasingly optimistic past roughly 45 degrees and 500 yards, where the flight path curves enough that a single flat correction stops fully capturing it.
What is the cosine of every angle from 5 to 60 degrees?
The rifleman's rule
horizontal distance = slant distance x cosine(angle from level). At 30 degrees, cosine(30) = 0.8660, so a 500 yard slant range is 500 x 0.8660 = 433.0 horizontal yards.
Exact trigonometry. The rifleman's rule is not the estimate here: treating the shot as equivalent to a level shot at that horizontal distance is the estimate, and it is a good one at ordinary hunting angles.
The cosine of the shooting angle falls from 0.9962 at 5 degrees to 0.5000 at 60 degrees, meaning a 60 degree shot covers only half its slant distance horizontally.
Sourced figure
| Angle | Cosine | Horizontal reduction |
|---|---|---|
| 5 deg | 0.9962 | 0.4 percent |
| 10 deg | 0.9848 | 1.5 percent |
| 15 deg | 0.9659 | 3.4 percent |
| 20 deg | 0.9397 | 6.0 percent |
| 25 deg | 0.9063 | 9.4 percent |
| 30 deg | 0.8660 | 13.4 percent |
| 35 deg | 0.8192 | 18.1 percent |
| 40 deg | 0.7660 | 23.4 percent |
| 45 deg | 0.7071 | 29.3 percent |
| 50 deg | 0.6428 | 35.7 percent |
| 55 deg | 0.5736 | 42.6 percent |
| 60 deg | 0.5000 | 50.0 percent |
Horizontal reduction is 1 minus the cosine, expressed as a percentage of the slant range. Every value here is exact arithmetic, computed directly from the angle: nothing is rounded from a lookup table.
What is the horizontal equivalent of a slant range shot?
Applying the cosine above to four common slant ranges a laser rangefinder might actually read on an incline.
A 500 yard slant range shot at 45 degrees is a 353.6 yard shot horizontally, and the same slant range at 60 degrees is only 250.0 horizontal yards, exactly half.
Sourced figure
| Angle | 200 yd slant | 300 yd slant | 500 yd slant | 800 yd slant |
|---|---|---|---|---|
| 5 deg | 199.2 yd | 298.9 yd | 498.1 yd | 797.0 yd |
| 10 deg | 197.0 yd | 295.4 yd | 492.4 yd | 787.8 yd |
| 15 deg | 193.2 yd | 289.8 yd | 483.0 yd | 772.7 yd |
| 20 deg | 187.9 yd | 281.9 yd | 469.8 yd | 751.8 yd |
| 25 deg | 181.3 yd | 271.9 yd | 453.2 yd | 725.0 yd |
| 30 deg | 173.2 yd | 259.8 yd | 433.0 yd | 692.8 yd |
| 35 deg | 163.8 yd | 245.7 yd | 409.6 yd | 655.3 yd |
| 40 deg | 153.2 yd | 229.8 yd | 383.0 yd | 612.8 yd |
| 45 deg | 141.4 yd | 212.1 yd | 353.6 yd | 565.7 yd |
| 50 deg | 128.6 yd | 192.8 yd | 321.4 yd | 514.2 yd |
| 55 deg | 114.7 yd | 172.1 yd | 286.8 yd | 458.9 yd |
| 60 deg | 100.0 yd | 150.0 yd | 250.0 yd | 400.0 yd |
Each cell is the slant range multiplied by the cosine of that row's angle. Use the horizontal figure with a level trajectory table or the bullet drop calculator, not the slant range a rangefinder displayed.
Why do steep shots go high if you dial the slant range?
Gravity has less horizontal distance to act over than the slant range suggests, so the bullet has actually fallen less than a correction computed for the full slant range assumes. Dial the correction for 500 yards on a shot that is really 353.6 horizontal yards at 45 degrees and the bullet strikes well above the point of aim. This is a common miss on steep mountain and treestand shots specifically because the rangefinder correctly reports the longer slant distance and the shooter dials it as though the shot were level.
A rangefinder with an angle compensation mode, such as the Leupold RX-1400i TBR/W Gen 2 Rangefinder with Flightpath, applies this same cosine correction automatically and reports the equivalent horizontal range directly, which removes the mental math from a shot that is already awkward to take.
Sources
- The rifleman's rule (cosine rule) for inclined fire, exact trigonometry for the horizontal component of a slant range
- Standard trigonometric cosine values, computed directly rather than read from a rounded table
Frequently asked questions
Does shooting uphill or downhill change the drop the same way?
Yes. The rifleman's rule uses the cosine of the angle, and cosine treats a positive uphill angle and a negative downhill angle identically because cosine is an even function. A 30 degree uphill shot and a 30 degree downhill shot at the same slant range use the exact same horizontal equivalent and the exact same correction.
What angle actually starts to matter for a hunting shot?
Under about 15 degrees the horizontal reduction is under 3.5 percent, which is smaller than most rifles' group size at typical hunting distances and safely ignorable. Past 30 degrees the reduction passes 13 percent and starts changing the correction by a meaningful fraction of the total drop, which is where a treestand or mountain shot needs the adjustment applied.
Is the rifleman's rule exact?
The cosine calculation is exact trigonometry. Treating the result as equivalent to a level shot at that horizontal distance is an approximation on top of it, a very good one at ordinary hunting angles and distances, and one that becomes noticeably optimistic past roughly 45 degrees and 500 yards where the true curved flight path diverges more from a flat approximation.
Do I need to know the exact angle, or is a rough guess fine?
A rough guess is usually fine below about 20 degrees, where cosine changes slowly and a few degrees of error barely moves the result. Past 30 degrees cosine falls more steeply with angle, so an angle compensating rangefinder or a simple angle indicator on the rifle becomes worth having rather than estimating by eye.
How does an angle compensating rangefinder work?
It measures the slant range with its laser and the angle from level with an internal inclinometer, then multiplies the two exactly as this page does and displays the horizontal equivalent directly. The shooter dials or holds for the displayed number as though it were a normal level range, with the angle math already applied.
Does angle affect wind drift the same way it affects drop?
No, and this is a common point of confusion. Wind drift depends on time of flight and the crosswind component of the actual wind, neither of which the shooting angle changes directly. Angle mainly affects vertical drop through the horizontal distance gravity acts over; wind calls are worked out separately, as covered on the wind drift chart.
Researched, not professional advice. This page is compiled from published manufacturer specifications, published optical and ballistic formulas, and owner-review consensus, not hands-on testing. Figures described as a rule of thumb are shooter convention rather than sourced numbers, and they are labelled that way wherever they appear. Ballistic figures come from a point mass model using the ballistic coefficient the maker publishes, so treat them as a starting point and confirm them on paper at a measured distance. Confirm your firearm is unloaded with the action open before you mount, level, torque or bore sight anything. Verify a zero only on a supervised range or a safe, legal backstop, know what lies beyond your target, and follow the law where you hunt and shoot, including rules on land access and permitted cartridges.