Ballistic Coefficient Calculator
Determine how well a projectile overcomes air resistance in flight
Calculate BC from mass, cross-sectional area, and drag coefficient using B = m/(C×A)
Ballistic Coefficient
What is ballistic coefficient?
The ballistic coefficient (BC) is essentially a projectile's "air resistance report card." It tells you how well a bullet, arrow, or any flying object can push through the atmosphere without slowing down too quickly.
🎯 Think of it this way: a sleek, heavy bullet with a high BC slices through the air like a hot knife through butter. A lightweight, blunt object with a low BC? That's more like throwing a beach ball into the wind.
A higher BC means the projectile retains its velocity better over distance, experiences less wind drift, and generally flies flatter. For long-range shooters, this translates to more predictable trajectories and easier holdover adjustments.
On the flip side, sometimes you want a low BC — like when designing spacecraft reentry vehicles that need to slow down quickly to avoid burning up or impacting too hard.
Understanding ballistics: the three phases
Before diving deeper into BC, it helps to understand where it fits in the bigger picture. Ballistics — the science of projectile motion — is typically divided into three phases:
Internal Ballistics
What happens inside the barrel or launcher — the propulsion phase before the projectile exits.
External Ballistics
The projectile's journey through the air — gravity, wind, and air resistance all come into play. BC lives here.
Terminal Ballistics
What happens when the projectile hits its target — penetration, expansion, energy transfer.
Want to explore the full trajectory? Try our Projectile Motion Calculator to see how launch angle, velocity, and gravity affect range and height.
The ballistic coefficient formula
The ballistic coefficient combines three physical properties into one number:
Ballistic Coefficient Formula
B = m / (C × A)
Where B = ballistic coefficient, m = projectile mass, C = drag coefficient, and A = cross-sectional area.
Breaking down each variable:
- Mass (m): Heavier projectiles carry more momentum and resist deceleration better. Units: grams, grains, kilograms.
- Cross-sectional area (A): The frontal area facing the airflow. Smaller = less drag. Units: mm², in², m².
- Drag coefficient (C): A dimensionless number describing the projectile's aerodynamic efficiency. Shape matters a lot here.
📊 The result is typically measured in kg/m² (SI) or lb/in² (imperial). This calculator supports both unit systems.
How to use this calculator
This calculator works bi-directionally — you can solve for any of the four variables by entering the other three. Here's how:
Enter the projectile mass (m)
Input the mass of your bullet, arrow, or projectile. Select your preferred unit (grams, grains, kilograms, etc.).
Enter the cross-sectional area (A)
This is the frontal area perpendicular to the direction of flight. For bullets, it's typically calculated from the caliber diameter.
Enter the drag coefficient (C)
Use a reference value based on projectile shape, or look up the specific value from manufacturer data. See the reference table below.
Read the ballistic coefficient (B)
The calculator automatically computes B. The result box highlights to show which value is being calculated.
Need to find the required mass for a target BC? Just enter the BC, area, and drag coefficient — the calculator will solve for mass automatically!
Worked example: calculating BC for a round projectile
Let's calculate the ballistic coefficient for a spherical projectile — like a musket ball or paintball — weighing 50 grams with a 13mm diameter.
Given information:
- Mass: m = 50 g
- Diameter: D = 13 mm
- Shape: sphere → C ≈ 0.47 (smooth) to 0.51 (rough)
Calculate cross-sectional area
A = π × D² / 4 = π × 13² / 4 = 132.73 mm²
Input values into the calculator
Enter m = 50 g, A = 132.73 mm², C = 0.51
Read the result
B = m / (C × A) = 50 / (0.51 × 132.73) ≈ 738.6 kg/m² or 1.05 lb/in²
📈 Interpretation: This BC of ~1.05 lb/in² is relatively high for a round ball, meaning it will retain velocity reasonably well. However, streamlined bullets typically achieve BC values of 0.3–0.6 lb/in² while being much more aerodynamically efficient.
Real-world applications
Long-range shooting
High-BC bullets maintain velocity for accurate shots at 1,000+ yards. Precision shooters select bullets based on BC for predictable trajectories.
Archery optimization
Arrow builders tweak point weight, shaft diameter, and fletching to achieve optimal BC for their shooting style and distance.
Spacecraft reentry
Engineers design reentry vehicles with low BC to maximize atmospheric braking and ensure safe landing speeds.
Sports equipment
Golf balls, baseballs, and javelins are all designed with aerodynamics in mind. BC helps predict flight behavior.
Military applications
ICBMs and artillery shells use high BC to minimize wind interference and maintain kinetic energy at impact.
Physics education
BC calculations help students understand the interplay between mass, shape, and air resistance in projectile motion.
The low Earth orbit satellite EYESAT-I has a BC of only about 0.072 lb/in², while a .50 caliber low-drag bullet can reach 1.062 lb/in². That's over 14× difference in air resistance characteristics!
Drag coefficient reference table
The drag coefficient (C) varies significantly based on shape. Here are common values to help you get started:
| Shape | Drag Coefficient (C) | Notes |
|---|---|---|
| Smooth sphere | ~0.47 | Golf balls, round bullets |
| Rough sphere | ~0.51 | Textured ball surfaces |
| Pointed bullet (G1) | ~0.295 | Most common rifle bullet reference |
| Boat-tail bullet (G7) | ~0.22 | Long-range match bullets |
| Streamlined body | ~0.04 | Optimal aerodynamic shapes |
| Flat plate (perpendicular) | ~1.28 | Maximum drag scenario |
| Cylinder (long axis parallel) | ~0.82 | Arrows, darts (simplified) |
⚠️ These are approximate values. Real drag coefficients depend on velocity (Reynolds number), surface roughness, and exact geometry. For precision work, use manufacturer-provided or wind-tunnel-tested values.
Tips & best practices
Use manufacturer data when available
Bullet and arrow manufacturers often publish BC values. These are measured, not estimated, and will be more accurate than calculations.
Know your drag model (G1 vs G7)
G1 is standard for most bullets; G7 is better for boat-tail designs. Don't mix them — comparing G1 to G7 values is apples to oranges.
Higher isn't always better
For hunting at moderate ranges, ultra-high BC bullets may be overkill. Terminal performance (expansion, penetration) matters too.
Calculate area accurately
For circular cross-sections, use A = π × (d/2)². Measure diameter carefully — small errors compound in the final BC.
Once you have the BC, use our Momentum Calculator to analyze impact energy and see how velocity loss affects terminal performance.
Frequently Asked Questions
What is ballistic coefficient in simple terms?
It's a number that tells you how well a projectile can push through air. Higher BC = less slowdown, less wind drift, flatter trajectory.
Should ballistic coefficient be high or low?
It depends on your goal. For long-range accuracy (bullets, arrows), higher is better. For spacecraft reentry or parachutes, lower is preferred to slow down quickly and safely.
What are the units for ballistic coefficient?
BC is typically measured in kg/m² (SI units) or lb/in² (imperial). This calculator supports both and converts automatically.
How do I calculate the ballistic coefficient manually?
Use the formula B = m / (C × A). Multiply drag coefficient by cross-sectional area, then divide mass by that product.
What is a G1 ballistic coefficient?
G1 is a standard drag model based on a specific projectile shape (flat-base, tangent ogive nose). It's the most commonly used reference for rifle bullets. G7 is another model better suited for boat-tail bullets.
How do I find the drag coefficient for my projectile?
Use the reference table above for common shapes. For precise values, check manufacturer specs or use computational fluid dynamics (CFD). Wind tunnel testing provides the most accurate results.
Does BC change with velocity?
Yes, technically. The drag coefficient varies with speed (especially near the speed of sound). Manufacturer BC values are often averaged across a velocity range. For extreme precision, use velocity-specific BC data.
Can I use this calculator for arrows?
Absolutely! Enter the arrow's total mass, the frontal area (based on shaft diameter), and an appropriate drag coefficient for the arrow profile. It works for any projectile.
Limitations & sources
- •This calculator uses a simplified model. Real-world BC depends on velocity, altitude, temperature, and other factors.
- •Drag coefficients are approximations. For precision applications, use measured values from manufacturers or testing.
- •The formula assumes stable flight. Tumbling or yawing projectiles have different aerodynamic behavior.
- •Results are for educational and planning purposes. Always verify critical calculations with professional tools or experts.
External references / further reading
Links provided for educational reference. This calculator uses standard physics formulas widely accepted in ballistics.
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