Speed Converter — m/s mph km/h RPM to linear

Choosing the wrong speed unit — or misreading the relationship between rotational and linear motion — can sink a motor selection or blow a conveyor design. Use this Speed Velocity Converter to convert between m/s, km/h, mph, ft/s, and RPM to linear speed using your input value, unit selection, and radius (for RPM). It matters across mechanical design, motor sizing, and automation system integration — anywhere rotational motion drives linear output. This page includes the conversion formulas, a worked belt conveyor example, full technical analysis, and an FAQ.

What is speed unit conversion?

Speed unit conversion is the process of expressing the same rate of motion in different measurement units — for example, converting 10 m/s into km/h or mph. When a motor spins at a known RPM, converting that to a linear speed tells you how fast the driven component actually moves.

Simple Explanation

Think of a bicycle wheel: the faster it spins (RPM), and the bigger the wheel (radius), the faster the bike moves forward — that forward speed is the linear velocity. Converting speed units is just re-labeling the same physical motion using a different measuring stick, like switching from miles to kilometers on a road sign. Nothing about the actual motion changes; only the number and the unit do.

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System Diagram

Speed Velocity Converter Calculator

How to Use This Calculator

1. Enter your speed value in the Speed Value field.
2. Select the unit you are converting from using the From Unit dropdown — choose m/s, km/h, mph, ft/s, or RPM.
3. If you selected RPM, enter the Radius of the rotating component in meters.
4. Click Calculate to see your result.

📹 Video Walkthrough — How to Use This Calculator

Mathematical Formulas

Use the formula below to calculate linear velocity from rotational speed.

The fundamental relationship between rotational and linear velocity is given by:

Where:

• v = linear velocity (m/s)
• ω = angular velocity (rad/s)
• r = radius (m)

Common unit conversions:

• 1 m/s = 3.6 km/h
• 1 m/s = 2.237 mph
• 1 m/s = 3.281 ft/s
• 1 RPM = π/30 rad/s

Simple Example

A motor spins at 300 RPM and drives a pulley with a radius of 0.1 m.

ω = 300 × (2π / 60) = 31.42 rad/s

v = ωr = 31.42 × 0.1 = 3.142 m/s

That equals 11.31 km/h, 7.03 mph, or 10.31 ft/s.

Technical Analysis and Applications

Understanding speed and velocity conversions is fundamental to mechanical engineering and automation design. This speed velocity converter serves as an essential tool for engineers working with rotating machinery, linear actuators, and motion control systems.

Fundamental Principles

The relationship between rotational and linear motion forms the basis of countless mechanical systems. When a wheel, pulley, or gear rotates, any point on its circumference travels at a linear velocity determined by the angular velocity and radius. This principle is crucial for designing belt drives, gear trains, and converting rotary motor motion to linear motion.

The formula v = ωr represents one of the most important relationships in mechanics. Angular velocity (ω) measured in radians per second, when multiplied by the radius, gives the linear velocity of a point at that radius from the center of rotation. This relationship allows engineers to precisely calculate the linear speed of belt systems, the surface speed of rotating drums, or the linear velocity achieved by rack and pinion systems.

Practical Applications in Automation

In industrial automation, speed conversions are essential for system design and component selection. When designing conveyor systems, engineers must convert between the motor's RPM and the desired belt speed in m/s or ft/min. Similarly, when selecting FIRGELLI linear actuators for precise positioning applications, understanding the relationship between rotational motor speed and linear actuator velocity is crucial for achieving desired cycle times.

Servo motor applications frequently require speed conversions when calculating the required angular velocity to achieve specific linear motion profiles. For example, in CNC machining, the spindle RPM must be converted to surface cutting speed to optimize machining parameters and tool life.

Design Considerations

When working with speed conversions, several engineering factors must be considered. Mechanical efficiency losses in gearboxes and drive systems mean that theoretical calculations must be adjusted for real-world performance. Typically, gear reducers operate at 90-98% efficiency, belt drives at 95-98%, and direct drive systems approach 99% efficiency.

Safety factors are critical when designing high-speed systems. The relationship between rotational and linear velocity means that small increases in RPM can result in significant increases in linear speed, potentially creating safety hazards or exceeding material limits. Engineers must carefully consider maximum safe operating speeds for all system components.

Worked Example: Belt Conveyor Design

Consider designing a belt conveyor system that must move products at 0.5 m/s using a motor operating at 1800 RPM through a gearbox with a 15:1 reduction ratio, driving a 200mm diameter drum.

First, calculate the drum RPM:

Drum RPM = Motor RPM ÷ Gear Ratio = 1800 ÷ 15 = 120 RPM

Convert RPM to rad/s:

ω = 120 × (2π/60) = 12.57 rad/s

Calculate linear belt speed:

v = ωr = 12.57 × 0.1 = 1.257 m/s

This exceeds our target speed of 0.5 m/s, so we would need either a larger gear reduction ratio or a smaller drum diameter to achieve the desired belt speed.

Integration with Linear Actuator Systems

Modern linear actuator systems often combine rotary motors with lead screws or ball screws to convert rotational motion to linear motion. The pitch of the screw determines the linear distance traveled per revolution, creating another layer of speed conversion. For a motor running at N RPM driving a lead screw with pitch P (mm per revolution), the linear velocity is:

Linear velocity (mm/s) = (N × P) ÷ 60

This relationship is fundamental when selecting actuators for specific application requirements, ensuring that the chosen system can achieve the required linear speeds within the motor's operating range.

Advanced Considerations

In precision applications, factors such as backlash, elastic deformation, and thermal expansion can affect the actual relationship between rotational and linear motion. High-precision systems may require feedback control to compensate for these effects and maintain accurate speed control.

Variable frequency drives (VFDs) allow precise control of motor RPM, enabling real-time adjustment of linear speeds in automated systems. Understanding speed conversions allows engineers to program VFDs with the correct parameters to achieve desired linear velocities.

For systems operating at high speeds, dynamic effects such as centrifugal forces, vibration, and resonance frequencies become important considerations. The speed velocity converter helps engineers identify critical speeds where these effects may become problematic.

Frequently Asked Questions

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