Physics calculators

Ballistic Calculator

Updated Jul 8, 2026 By Jehan Wadia
Rate Formulas
Unit System
Input Units
Mixed: yards for range, inches for drop, fps for velocity.
Output Drop / Drift Columns
Pick one or more angular/linear output columns.
Load / Ammunition
Drag Model
G1 suits most flat-base/older designs. G7 is recommended for boat-tail bullets beyond ~500 yd.
Firearm / Optics
Bore centerline to optic centerline.
Format "1:X" — used for stability & spin drift.
Environment / Atmosphere
+ uphill / − downhill.
Wind Clock Reference
12 3 6 9
Arrow points to the direction the wind blows from.
Range Card Configuration

Solution Summary

Zero Angle (Super-elevation)
—
Drop @ Max Range
—
Remaining Velocity @ Max
—
Transonic / Supersonic Range
—
Step-by-Step Solution
Range Card
Signs: bullet drop below the line of sight is negative. Wind/drift positive = right, negative = left.
Trajectory Chart
Scope Adjustment / Dial-Up Calculator
Elevation: —
Windage: —

Introduction

This free ballistic calculator builds a full range card for any rifle load. Enter your bullet, muzzle velocity, zero range, and weather conditions, and the tool solves for bullet drop, wind drift, remaining velocity, and energy at every distance you choose. Results are shown in MOA, MIL, and linear units so you can dial your scope or hold with confidence.

The calculator uses point-mass trajectory integration with standard G1 and G7 drag models. It accounts for air density, altitude, humidity, temperature, shot angle, and barrel twist. Advanced options let you add spin drift and Coriolis corrections for extreme long-range shooting. A built-in stability estimator checks whether your barrel twist rate is right for your bullet using the Miller formula.

Pick a factory load from the built-in library or type in your own handload data. Switch between imperial and metric units at any time. The tool generates a drop chart, a trajectory graph, and a scope click calculator — everything you need to shoot accurately at distance.

How to Use Our Ballistic Calculator

Enter your bullet, firearm, and weather details below to get a full range card, trajectory chart, bullet drop, wind drift, and scope adjustments for any distance.

Unit System: Pick Imperial (yards, inches, fps), Metric (meters, cm, m/s), or Mixed (yards for range, inches for drop, fps for velocity). This sets how all numbers are shown. If you need to convert temperature values between systems, our Celsius to Fahrenheit calculator or Fahrenheit to Celsius calculator can help.

Output Columns: Check the boxes for how you want drop and drift shown in your range card. Choose Linear (inches or cm), MOA, MIL, or any mix of the three.

Load Type: Pick Factory Load to choose from a built-in list of common bullets. Pick Handload if you want to type in your own bullet data.

Caliber: If using a factory load, select your caliber first. The tool will then fill in bullet style, weight, and muzzle velocity options for you.

Bullet Style: Choose the bullet design that matches your ammo, such as Boat Tail, ELD-M, or OTM.

Bullet Weight: Select the grain weight of your bullet.

Muzzle Velocity: Choose or enter the speed of the bullet as it leaves the barrel. If you need to work with speed, distance, and time relationships separately, try our speed distance time calculator.

Ballistic Coefficient (BC): If using a handload, enter your bullet's BC value. This number tells the calculator how well your bullet cuts through the air.

Drag Model: Pick G1 for flat-base or traditional bullets. Pick G7 for boat-tail or long-range bullets. G7 is more accurate at longer distances for sleek bullets.

Sight Height: Enter the distance from the center of your bore to the center of your scope. Most rifle setups are about 1.5 inches.

Zero Range: Enter the distance at which your rifle is zeroed. This is the range where your point of aim and point of impact are the same.

Barrel Twist: Enter your barrel's twist rate in the format 1:X (for example, 1:10). This is used to figure out spin drift and bullet stability.

Cant Angle: Enter how many degrees your rifle is tilted to the side. Set this to 0 if you hold your rifle level. For general angle computations, see our angle calculator.

Temperature: Enter the current air temperature. Hotter air is thinner, so bullets fly farther. Colder air is denser and slows bullets down more.

Altitude: Enter your elevation above sea level. Higher altitude means thinner air and less drag on the bullet. Our density altitude calculator can help you understand how altitude and temperature combine to affect air density.

Humidity: Enter the relative humidity as a percent from 0 to 100. Humid air is slightly thinner than dry air. You can use our relative humidity calculator to determine your current humidity if you have other weather readings.

Wind Speed: Enter how fast the wind is blowing. This is used to calculate how far the wind pushes your bullet off course. Our crosswind calculator can also help you break wind into headwind and crosswind components.

Wind Direction: Pick the clock position the wind is blowing from. For example, 9 o'clock means the wind comes from your left. 3 o'clock means it comes from your right.

Inclination / Shot Angle: Enter your uphill or downhill angle in degrees. Use a positive number for uphill and a negative number for downhill. Leave at 0 for flat ground.

Start Range: Set the first distance you want shown on your range card. Most people start at 0.

Maximum Range: Set the farthest distance you want the range card to calculate out to.

Range Step: Set the distance between each row on the range card. For example, 50 means the card shows data every 50 yards or meters.

Spin Drift (Advanced): Turn this on to include the small sideways drift caused by the bullet's spin. This matters most at long range.

Coriolis / Eötvös (Advanced): Turn this on to include the effect of the Earth's rotation on your bullet. Enter your latitude and firing direction when enabled. This only matters at very long range.

Atmospheric Model (Advanced): Choose User-Defined to use the temperature and altitude you entered. Choose ICAO Standard to use the international standard atmosphere based on altitude alone.

Bullet Length (Stability Estimator): Enter the total length of your bullet. The calculator uses this along with your other inputs to estimate the bullet's gyroscopic stability factor.

Scope Adjustment Calculator: After you calculate, pick a target range from the dropdown. Enter your scope's click values for MOA and MIL. The tool then shows exactly how many clicks of elevation and windage to dial.

Once all your data is entered, press the Calculate Range Card button. The calculator will display a solution summary, step-by-step math, a full range card table, a trajectory chart, and scope dial-up values. Press Reset / Clear All to return every field to its default setting.

What Is a Ballistic Calculator?

A ballistic calculator helps shooters figure out where a bullet will hit at different distances. When a bullet leaves a gun, it does not fly in a straight line. Gravity pulls it down, air slows it down, and wind pushes it sideways. This tool does the math for all of those forces so you know exactly how to aim. The physics behind a bullet's flight path shares many principles with general projectile motion, though ballistic calculations add aerodynamic drag and atmospheric effects that simple projectile equations do not cover.

How Bullet Drop Works

The moment a bullet exits the barrel, gravity starts pulling it toward the ground — the same constant acceleration that governs all falling objects. You can explore this principle in isolation with our free fall calculator. The farther the target, the more the bullet drops. To hit a distant target, you must aim slightly above it. The exact amount depends on the bullet's speed, weight, shape, and the drag model used — either G1 or G7. G1 works well for flat-base bullets. G7 is better for modern boat-tail bullets used in long-range shooting.

Why Wind and Weather Matter

Wind pushes a bullet off course. A 10 mph crosswind can move a bullet several inches at just a few hundred yards. Temperature, altitude, and humidity also change how thick the air is. Thinner air at high altitude or on hot days means less drag, so the bullet drops less. Thick, cold air at sea level creates more drag and more drop. Pilots and long-range shooters both pay close attention to density altitude because it directly determines how much resistance the atmosphere puts on a projectile. Weather conditions such as the dew point and wind chill can also help you gauge current atmospheric conditions before heading to the range.

What Is a Ballistic Coefficient?

A ballistic coefficient (BC) is a number that tells you how well a bullet cuts through air. A higher BC means the bullet keeps its speed longer and drops less over distance. Long, sleek bullets have high BCs. Short, blunt bullets have low BCs. You can find the BC for your bullet on the manufacturer's box or website. Because BC governs how quickly a bullet decelerates, it directly affects the kinetic energy and momentum the bullet retains at any given range.

Zeroing and Scope Adjustments

When you zero a rifle, you set it so the bullet hits exactly where you aim at one specific distance — usually 100 yards. At any other distance, you need to adjust. This calculator gives you those adjustments in MOA (minutes of angle) or MIL (milliradians), which match the clicks on most rifle scopes. It also tells you the exact number of clicks to dial for any range in your table.

Bullet Stability

A bullet must spin fast enough to stay stable in flight. The spin comes from the rifling grooves inside the barrel. If the twist rate is too slow for a long, heavy bullet, it will wobble and lose accuracy. The stability factor (Sg) in this calculator tells you if your barrel twist is a good match for your bullet. A value between 1.4 and 2.0 is ideal. The underlying physics of rotational stability also connects to concepts like torque and moment of inertia, which describe how objects resist changes in their spinning motion.

Formulas used

Point-mass drag deceleration
a_{\text{drag}} = \frac{K \cdot \sigma \cdot C_d(M) \cdot V_r^2}{BC}, \quad K = 0.0877275 \, \rho_{\text{std}}
Air density ratio
\sigma = \frac{P}{P_0} \cdot \frac{T_0}{T_R} \cdot \left(1 - \frac{0.378 \, e}{P}\right), \quad P = P_0\left(1 - 6.8756 \times 10^{-6} \, h\right)^{5.2559}
Speed of sound
a = 49.0223 \sqrt{T_R}
Miller gyroscopic stability factor
S_g = \frac{30\, m}{t^2 \, d^3 \, l\,(1 + l^2)} \cdot \left(\frac{V}{2800}\right)^{\!1/3} \cdot \frac{1}{\sigma}, \quad t = \frac{\text{twist}}{d},\; l = \frac{L}{d}
Kinetic energy
E = \frac{1}{2} \cdot \frac{m}{7000 \cdot g} \cdot V^2
Spin drift (Litz approximation)
\Delta_s = 1.25\,(S_g + 1.2)\, t^{1.83}
Coriolis / Eötvös deflection
\Delta_{\text{horiz}} = \Omega \sin\phi \cdot x \cdot t, \quad \Delta_{\text{vert}} = \Omega \cos\phi \, \sin\alpha \cdot x \cdot t
Angular conversion (MOA and MIL)
\text{MOA} = \frac{\Delta}{R} \times 3437.75, \quad \text{MIL} = \frac{\Delta}{R} \times 1000

Frequently asked questions

What drag model should I use, G1 or G7?

Use G1 for flat-base, round-nose, or older bullet designs. Use G7 for modern boat-tail, VLD, ELD-M, or hybrid bullets. G7 gives more accurate results past 500 yards for sleek, long-range bullets. If you are not sure, check your bullet maker's website — they usually say which model fits best.

Where do I find my bullet's ballistic coefficient?

Check the bullet box, the ammo maker's website, or the reloading manual. Most companies like Hornady, Sierra, and Berger list BC values for each bullet. Make sure you use the BC that matches your drag model — a G1 BC number is different from a G7 BC number for the same bullet.

How do I measure sight height?

Sight height is the distance from the center of your barrel bore to the center of your scope lens. For most bolt-action rifles with a scope, this is about 1.5 inches. You can measure it with a ruler from the top of the barrel to the middle of the scope tube. Some tall scope mounts push this to 1.7 or 2.0 inches.

What zero range should I use?

Most shooters zero at 100 yards (or 100 meters). This is the most common and works well for hunting and target shooting. Some long-range shooters use a 200-yard zero to reduce holdover at mid-range. Use whatever distance you actually zeroed your rifle at the range.

What does the transonic zone mean?

The transonic zone is where a bullet slows down to near the speed of sound — roughly 1,125 to 1,340 fps. In this zone, the air flow around the bullet becomes unstable and accuracy drops. The range card highlights these rows in yellow. If you need to hit targets past the transonic zone, pick a bullet with a higher BC that stays supersonic longer.

What is a good stability factor?

A stability factor (Sg) between 1.4 and 2.0 is ideal. Below 1.0 means the bullet is unstable and will tumble. Between 1.0 and 1.4 is marginal — it may work but accuracy could suffer. Above 2.0 means the bullet is over-stabilized, which can cause extra drag at very long range. If your Sg is too low, you need a faster twist barrel.

How does temperature affect my bullet's trajectory?

Hot air is thinner than cold air. In thin air, there is less drag on the bullet, so it drops less and keeps speed longer. Cold air is denser, which increases drag and makes the bullet drop more. A 20°F change in temperature can shift your point of impact by an inch or more at 300 yards.

Do I need to turn on spin drift and Coriolis?

For most shooting under 600 yards, no. These effects are very small at short and medium range. Turn on spin drift if you shoot past 800 yards. Turn on Coriolis only for extreme long-range shots past 1,000 yards. At normal hunting and target distances, these corrections are smaller than normal shot-to-shot variation.

What is the difference between MOA and MIL?

MOA (minute of angle) equals about 1.047 inches at 100 yards. MIL (milliradian) equals about 3.6 inches at 100 yards. Both are angular units used to adjust scopes. Most American hunting scopes use MOA clicks. Many tactical and long-range scopes use MIL clicks. Use whichever matches your scope.

How do I read the wind clock direction?

The wind clock uses a clock face. Imagine you are the center, facing 12 o'clock. A 9 o'clock wind blows from your left. A 3 o'clock wind blows from your right. A 12 o'clock wind is a headwind, and 6 o'clock is a tailwind. The 3 and 9 o'clock positions cause the most drift. Headwinds and tailwinds cause very little sideways push.

Can I use this calculator for handloads?

Yes. Switch to Handload / Custom mode at the top of the Load section. Then type in your bullet diameter, weight, muzzle velocity, bullet style, and ballistic coefficient. Make sure you enter the BC that matches your chosen drag model (G1 or G7).

Why does my bullet not reach the maximum range I set?

If the bullet slows down too much, it runs out of energy before it gets to your max range. The table will show a message saying the bullet did not reach that distance. This happens with light, low-BC bullets or very long maximum ranges. Try a shorter max range or use a bullet with a higher BC and faster muzzle velocity.

How do I find my barrel twist rate?

Check your rifle's manual, the manufacturer's website, or the markings on the barrel. It is usually stamped or printed as something like "1:10" or "1:8." The number after the colon is how many inches the bullet travels for one full spin. A lower number like 1:7 is a faster twist that stabilizes heavier bullets.

What does the cant angle do?

Cant angle is how much your rifle is tilted to one side. Even a small tilt shifts your bullet's impact both sideways and vertically. At long range, a 5-degree cant can move your shot several inches. If you use a bubble level on your scope, set this to 0. Otherwise, enter your estimated tilt.

How do I use the scope click calculator?

After you press Calculate, scroll to the Scope Adjustment section. Pick your target range from the dropdown. Enter your scope's click value — most scopes are 0.25 MOA or 0.1 MIL per click. The tool shows how many MOA or MIL to dial, and exactly how many clicks that equals for both elevation and windage.

What is the difference between ICAO and user-defined atmosphere?

User-defined uses the temperature, altitude, and humidity you type in. ICAO Standard uses the international standard atmosphere model, which calculates temperature and pressure based on altitude alone. Use user-defined for real-world accuracy. Use ICAO if you want a standard baseline or do not know the current weather.

Does altitude really matter for bullet drop?

Yes. At higher altitudes the air is thinner, so there is less drag on the bullet. A bullet fired at 5,000 feet above sea level will drop noticeably less than the same bullet fired at sea level. If you shoot in the mountains, always enter your altitude for the most accurate results.

Why does the chart show two lines?

The blue line shows bullet drop — how far below your line of sight the bullet falls at each distance. The green dashed line shows remaining velocity — how fast the bullet is still moving. Both are plotted against range so you can see how your bullet performs from muzzle to max distance.

Can I switch units after I already entered my data?

Yes. When you switch between Imperial and Metric, the calculator automatically converts all your numbers. Your data is not lost. You can switch back and forth at any time, and the range card and chart will update to show the new units.

What does the shot angle or inclination setting do?

When you shoot uphill or downhill, the bullet drops less than it would on flat ground. This is because gravity only pulls on the part of the flight path that is horizontal. Enter a positive number for uphill shots and a negative number for downhill shots. The calculator adjusts the drop using the cosine of your angle.