Understanding arrow speed is an important part of evaluating archery equipment and arrow performance. Whether you are comparing setups, reviewing changes in arrow weight, or simply trying to understand how draw weight and bow efficiency affect speed, having a quick calculation tool can make the process much easier.

The Arrow FPS Calculator provides an estimate of arrow velocity using several important inputs: arrow weight, draw weight, draw length, and bow efficiency. It can also use a known bow speed when that information is available. The results are presented in multiple useful units, including feet per second (FPS), meters per second (m/s), and kilometers per hour (km/h).

In addition to speed, the calculator estimates kinetic energy in foot-pounds and momentum in pound-feet per second. These measurements provide additional ways to understand the physical characteristics of an arrow in flight. Because the calculator uses an approximate energy model, its results should be treated as estimates rather than a substitute for chronograph measurements or manufacturer specifications.

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What Is an Arrow FPS Calculator?

An Arrow FPS Calculator is a tool designed to estimate how fast an arrow travels after being launched from a bow. FPS, or feet per second, is one of the most commonly used measurements for arrow velocity.

Arrow speed can be influenced by several factors, including:

• Arrow weight
• Bow draw weight
• Draw length
• Bow efficiency
• Bow design
• String and accessory weight
• Arrow setup
• Actual equipment condition

The calculator focuses on four major inputs that can be used to create an approximate velocity estimate. It also provides an optional method based on a known bow speed and a reference arrow weight.

The tool produces five main results:

Result	Unit
Estimated Arrow Speed	FPS
Arrow Speed	km/h
Arrow Speed	m/s
Kinetic Energy	ft-lb
Momentum	lb-ft/s

This makes the calculator useful for understanding several different aspects of arrow performance rather than focusing only on FPS.

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How to Use the Arrow FPS Calculator

Using the calculator is straightforward. You need to provide several basic measurements before calculating the estimated arrow performance.

Step 1: Enter Arrow Weight

The first input is Arrow Weight, measured in grains.

Arrow weight is a major factor in velocity calculations. A heavier arrow generally requires more energy to reach the same speed as a lighter arrow.

For example, you might enter:

Arrow Weight = 400 grains

Make sure you use the complete arrow weight relevant to your calculation.

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Step 2: Enter Draw Weight

Next, enter the bow’s Draw Weight in pounds (lb).

For example:

Draw Weight = 60 lb

Draw weight is used by the calculator as part of its approximate energy model. A greater draw weight can provide more potential energy under the model used by the calculator.

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Step 3: Enter Draw Length

Enter your Draw Length in inches.

For example:

Draw Length = 29 inches

Draw length is important because the calculator estimates potential bow energy using both draw weight and draw length.

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Step 4: Enter Bow Efficiency

Enter the estimated Bow Efficiency as a percentage.

The calculator uses 80% as the default value.

For example:

Bow Efficiency = 80%

Efficiency represents the portion of the estimated draw energy that is treated as being transferred into arrow kinetic energy in this simplified model.

Actual bow efficiency can vary depending on the bow, setup, arrow, accessories, and shooting conditions, so the value should be viewed as an estimate.

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Step 5: Enter Known Bow Speed if Available

The Known Bow Speed field is optional.

If you already know the speed of your bow with a particular reference setup, you can enter the known FPS value.

For example:

Known Bow Speed = 300 FPS

When a valid known speed is entered, the calculator uses the known-speed method rather than the approximate draw-energy method.

This can be particularly useful when you have a measured or manufacturer-provided speed for a reference arrow.

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Step 6: Enter Reference Arrow Weight

The calculator provides a Reference Arrow Weight field, with a default value of 350 grains.

This value is used when a known bow speed is supplied.

For example:

• Known bow speed = 300 FPS
• Reference arrow weight = 350 grains
• Actual arrow weight = 400 grains

The calculator adjusts the speed according to the relationship between the reference arrow weight and the actual arrow weight.

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Step 7: Click Calculate

After entering the required information, click Calculate.

The calculator displays:

1. Estimated arrow speed in FPS
2. Arrow speed in km/h
3. Arrow speed in m/s
4. Kinetic energy in ft-lb
5. Momentum in lb-ft/s

If you want to start a new calculation, the Reset option clears the current calculation by reloading the calculator.

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Arrow FPS Formula Explained

The calculator can use one of two calculation approaches depending on whether a known bow speed is entered.

Method 1: Known Bow Speed

When a valid known bow speed is entered, the calculator uses this formula:$$FPS = Known\ Speed \times \sqrt{\frac{Reference\ Arrow\ Weight}{Actual\ Arrow\ Weight}}$$

This means the estimated speed changes according to the ratio between the reference arrow weight and the actual arrow weight.

For example:

• Known speed = 300 FPS
• Reference arrow = 350 grains
• Actual arrow = 400 grains

The calculation becomes:$$FPS = 300 \times \sqrt{\frac{350}{400}}$$

The resulting estimate is approximately:$$FPS \approx 280.62$$

So the estimated speed would be about 280.62 FPS.

This simplified relationship illustrates why increasing arrow weight generally reduces estimated speed when other conditions remain the same.

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Method 2: Draw Energy and Bow Efficiency

If no known bow speed is entered, the calculator estimates arrow speed using draw weight, draw length, and bow efficiency.

The first calculation is an approximate draw energy:$$Draw\ Energy = Draw\ Weight \times Draw\ Length \times 0.5$$

The calculator then applies the selected efficiency:$$Arrow\ Energy = Draw\ Energy \times \frac{Efficiency}{100}$$

The resulting arrow energy is then used to estimate velocity:$$FPS = \sqrt{\frac{Arrow\ Energy \times 450240}{Arrow\ Weight}}$$

This approach gives an estimated velocity based on the simplified energy assumptions built into the calculator.

It is important to understand that this is not a complete physical model of a real bow. Real bows transfer energy through a complex interaction between the limbs, cams, string, arrow, draw force curve, and other components. Therefore, actual chronograph readings may differ from the calculator’s estimate.

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Kinetic Energy Formula

The calculator also determines the arrow’s kinetic energy.

The formula used is:$$KE = \frac{Arrow\ Weight \times FPS^2}{450240}$$

The result is displayed in foot-pounds (ft-lb).

Kinetic energy depends strongly on velocity because velocity is squared in the equation.

That means an increase in speed can have a significant effect on calculated kinetic energy.

For example, if all other factors remain constant, increasing velocity from 250 FPS to 300 FPS does more than simply increase kinetic energy by 20%, because the velocity term is squared.

This is one reason kinetic energy is useful alongside FPS when comparing arrow setups.

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Momentum Formula

The calculator also estimates arrow momentum.

Momentum can be represented as:$$p = mass \times velocity$$

The calculator first converts arrow weight from grains into pounds:$$Arrow\ Mass\ (lb) = \frac{Arrow\ Weight}{7000}$$

It then converts that value into slugs:$$Arrow\ Mass\ (slugs) = \frac{Arrow\ Mass\ (lb)}{32.174}$$

Finally:$$Momentum = Arrow\ Mass\ (slugs) \times FPS$$

The result is displayed as lb-ft/s.

Momentum provides another perspective on arrow motion because it depends on both mass and velocity.

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Arrow FPS Example

Let’s consider an example setup:

• Arrow weight: 400 grains
• Draw weight: 60 lb
• Draw length: 29 inches
• Bow efficiency: 80%
• Known bow speed: not entered
• Reference arrow weight: 350 grains

Because no known bow speed is entered, the calculator uses the approximate draw-energy method.

First, estimated draw energy is calculated:$$60 \times 29 \times 0.5 = 870$$

The calculator then applies 80% efficiency:$$870 \times 0.80 = 696$$

This energy estimate is then used with the 400-grain arrow weight to calculate an approximate FPS value.

The resulting FPS is then converted into:

• Meters per second
• Kilometers per hour

The same estimated velocity is also used to calculate kinetic energy and momentum.

The important point is that changing any of the primary inputs can change the final result.

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How Arrow Weight Affects FPS

Arrow weight has a major effect on estimated velocity.

When using the known-speed calculation, the calculator uses an inverse square-root relationship between arrow weight and speed.

In simple terms:

Heavier arrow → generally lower FPS

Lighter arrow → generally higher FPS

However, arrow speed should not be evaluated in isolation. A setup should be appropriate for the bow and intended use, and extremely light arrows can create equipment and safety concerns depending on the bow and manufacturer requirements.

Therefore, the fastest possible arrow is not automatically the best arrow setup.

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How Draw Weight Affects Arrow Speed

Draw weight is another important input.

Under the calculator’s approximate energy model, increasing draw weight increases estimated draw energy.

For example, if draw length remains constant, moving from a lower draw weight to a higher draw weight increases the energy estimate used by the calculator.

However, actual arrow speed depends on more than draw weight. Bow design, efficiency, arrow mass, and other equipment characteristics also affect real-world velocity.

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How Draw Length Affects the Calculation

Draw length is included in the calculator’s approximate energy calculation:$$Draw\ Energy = Draw\ Weight \times Draw\ Length \times 0.5$$

Under this model, a longer draw length increases the estimated energy available to the arrow.

However, draw length should be measured correctly rather than changed simply to produce a higher calculated FPS. Proper fit, shooting form, and equipment specifications are more important than maximizing a calculator result.

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Why Bow Efficiency Matters

The efficiency input represents how much of the calculated draw energy is treated as transferred to the arrow.

For example:

• 70% efficiency uses less energy than
• 80% efficiency
• 90% efficiency

within the calculator’s model.

The default value is 80%, but actual efficiency can vary substantially between equipment configurations.

For the most realistic estimate, use a reasonable efficiency value based on the bow and setup rather than selecting a high percentage simply to obtain a higher FPS.

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FPS, m/s, and km/h Conversion

The calculator provides speed in three units.

Feet Per Second

FPS is commonly used in archery discussions and equipment specifications.

Meters Per Second

The calculator converts FPS to m/s using:$$m/s = FPS \times 0.3048$$

For example:$$300 \times 0.3048 = 91.44\ m/s$$

Kilometers Per Hour

The calculator then converts meters per second into kilometers per hour:$$km/h = m/s \times 3.6$$

Therefore:$$91.44 \times 3.6 = 329.18\ km/h$$

These are simply different ways of expressing the same velocity.

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Why Use Both Kinetic Energy and Momentum?

FPS tells you how quickly the arrow is moving, but it does not describe everything about its motion.

Kinetic energy considers both arrow mass and velocity and is particularly sensitive to velocity because speed is squared in the formula.

Momentum considers mass and velocity directly.

Looking at both values can therefore provide a broader picture of the arrow’s calculated physical performance.

However, neither value alone should be treated as a complete measurement of real-world effectiveness. Arrow construction, broadhead selection, bow tuning, shot placement, and other factors can also matter greatly depending on the intended application.

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Practical Uses of an Arrow FPS Calculator

Comparing Different Arrow Weights

You can run multiple calculations using different arrow weights to see how estimated speed changes.

For example, compare:

• 350 grains
• 400 grains
• 450 grains

while keeping other inputs unchanged.

This can demonstrate the relationship between arrow mass and estimated velocity.

Understanding Bow Setup Changes

If draw weight or draw length changes, you can enter the new values and compare the estimated results.

This can help illustrate how individual variables affect the calculation.

Converting Velocity Units

If a specification is given in FPS but you prefer metric units, the calculator provides m/s and km/h automatically.

Estimating Energy

The kinetic-energy output provides another measurement for comparing calculated arrow setups rather than relying solely on FPS.

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Tips for Getting Better Results

Use an Accurate Arrow Weight

If possible, use the actual completed arrow weight rather than an approximate component weight.

Measure Draw Length Carefully

An incorrect draw-length value can influence the energy-based calculation.

Use a Realistic Efficiency Value

The default 80% is an assumption used by the calculator. If you have better information about your specific setup, use a more appropriate value.

Use Chronograph Data When Available

A chronograph measurement from your actual equipment is generally more useful for determining real arrow speed than a theoretical estimate.

Keep Comparisons Consistent

When comparing two arrow setups, change one important variable at a time when possible. This makes it easier to understand what caused the difference.

Check Manufacturer Specifications

Always follow the bow manufacturer’s recommendations for arrow weight, draw weight, and equipment configuration.

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Estimated Speed vs. Actual Speed

One of the most important limitations of an Arrow FPS Calculator is that calculated speed is an estimate.

Actual arrow speed can be influenced by factors that are not fully represented in a simplified calculator, including:

• Bow model
• Cam system
• String and cable condition
• Arrow construction
• Fletching
• Nock
• Point weight
• Accessories
• Tuning
• Temperature
• Shooting technique
• Actual energy-transfer efficiency

For this reason, two bows with the same listed draw weight and draw length may not produce exactly the same arrow speed.

If precise velocity matters, measuring the actual setup with a suitable chronograph is preferable.

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Arrow FPS Quick Reference

Factor	General Effect on Estimated Speed
Higher arrow weight	Usually lowers FPS
Lower arrow weight	Usually raises FPS
Higher draw weight	Increases estimated energy
Longer draw length	Increases estimated energy in this model
Higher efficiency	Increases estimated energy
Higher known bow speed	Raises calculated reference-based speed
Higher reference arrow weight	Raises the reference-based estimate for a fixed actual arrow weight

These relationships describe the calculator’s mathematical model and should not be interpreted as guarantees of real-world bow performance.

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Frequently Asked Questions

1. What does FPS mean in archery?

FPS means feet per second. It describes how many feet an arrow travels in one second. It is a commonly used unit for discussing arrow velocity and bow performance.

2. What information do I need to use the Arrow FPS Calculator?

You need arrow weight, draw weight, draw length, and bow efficiency. Known bow speed is optional. The calculator uses a default reference arrow weight of 350 grains, which can also be changed.

3. Does a heavier arrow fly slower?

Generally, yes, when other conditions remain similar. The calculator’s known-speed method specifically uses an inverse square-root relationship between arrow weight and estimated velocity.

4. What is the default bow efficiency?

The calculator starts with 80% efficiency. This is an input assumption for the approximate energy model and may not represent the actual efficiency of every bow and setup.

5. What is a good arrow FPS?

There is no single ideal FPS for every archer or setup. Appropriate arrow speed depends on the bow, arrow weight, manufacturer specifications, intended use, tuning, and other factors. A higher FPS is not automatically better.

6. Why does the calculator show kinetic energy?

Kinetic energy provides additional information about the arrow’s calculated motion. The calculator determines it from arrow weight and estimated velocity and displays the result in foot-pounds.

7. What is arrow momentum?

Arrow momentum represents the relationship between the arrow’s mass and velocity. The calculator converts the arrow’s grain weight into mass units and multiplies the resulting mass by velocity.

8. What happens if I enter a known bow speed?

If a valid known bow speed is entered, the calculator uses that value with the reference arrow weight and actual arrow weight to estimate the arrow’s speed. This method takes priority over the approximate draw-energy calculation.

9. Is the calculated FPS exact?

No. It is an estimate. Real arrow speed can vary because of bow design, actual efficiency, arrow components, tuning, accessories, and other factors. A chronograph is better for measuring actual speed.

10. Can I use the calculator to compare different arrows?

Yes. You can enter different arrow weights while keeping the other inputs consistent and compare the estimated FPS, kinetic energy, and momentum. Always make sure the selected arrows meet the bow manufacturer’s requirements.

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Final Thoughts

The Arrow FPS Calculator provides a convenient way to explore the relationship between arrow weight, draw weight, draw length, bow efficiency, and arrow velocity. By entering your equipment information, you can obtain estimated FPS along with equivalent speeds in meters per second and kilometers per hour.

The calculator goes beyond velocity by also estimating kinetic energy and momentum. These additional measurements can help you understand how changes in arrow weight and speed affect the calculated physical characteristics of an arrow.

For planning and comparison, the tool can be very useful, but remember that calculated performance is not the same as measured performance. Actual bow and arrow setups can behave differently from simplified mathematical models. For precise velocity information, use reliable measurements from your actual equipment, follow manufacturer specifications, and prioritize safe, properly matched equipment over simply maximizing speed.