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

If you choose the wrong speed unit or mix up rotational and linear motion, you can end up with the wrong motor or a conveyor that won’t meet requirements. The Speed Velocity Converter here handles units like m/s, km/h, mph, ft/s, and RPM (which needs a radius for linear speed). This comes up in plenty of mechanical projects—motor sizing, conveyor layout, automation—basically anywhere you’re translating rotary to linear movement. You’ll find conversion formulas, a conveyor example, and some real-world engineering notes below.

What is speed unit conversion?

Speed unit conversion is simply changing how you express a rate of motion, such as turning 10 m/s into km/h or mph. If you know a motor’s RPM, converting to linear speed tells you how quickly the part it moves is actually traveling.

Simple Explanation

Picture a bicycle wheel: spin it faster or use a bigger wheel, and the bike moves quicker. That’s linear velocity. Swapping between units—like miles or kilometers for distance—doesn’t change the actual motion, just the number on your readout.

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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

Speed and velocity conversions show up everywhere in practical engineering. If you’re building machines with rotating parts, actuators, or setting up a control system, you’ll end up converting back and forth between how fast something rotates and how fast it moves linearly.

Fundamental Principles

Any time you have something rotating—a wheel, pulley, or gear—the surface speed depends on both how quickly it spins and its radius. This is the backbone of things like belts, gears, or translating a motor’s spin into linear action.

The equation v = ωr simply says that the farther you get from the center, the more distance you cover per revolution, and the faster your linear speed at a given angular speed. This is how you work out the speed of a conveyor, a drum surface, or even a pinion driving a rack.

Practical Applications in Automation

If you’re designing a conveyor, you need to turn the motor’s RPM into belt speed in m/s or ft/min. With actuators, knowing how a motor’s RPM translates into linear output lets you check if you’ll hit cycle time targets. The same logic crops up in servo motor setups—when you need a certain movement profile, you’re often solving for what angular speed gives you the needed linear speed. Even with CNC spindles, RPM needs to be tied back to actual cutting speed at the tool edge.

Design Considerations

Real systems don’t transfer 100% of speed cleanly—gearboxes, belts, and chains each drop a bit of energy. Typical working ranges are 90-98% for gearboxes, 95-98% for belts, and close to 99% for direct drives, but check your own setup. Also, increases in RPM stack up quickly on the linear side because velocity scales directly with speed and radius, which can lead to exceeding what materials or guards are rated to handle.

Worked Example: Belt Conveyor Design

Say you need a conveyor to move at 0.5 m/s. You’ve got a motor spinning at 1800 RPM, geared down 15:1, turning a drum 200mm in diameter.

First, get your drum RPM:

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

Convert to rad/s:

ω = 120 × (2π/60) = 12.57 rad/s

Calculate belt speed:

v = ωr = 12.57 × 0.1 = 1.257 m/s

This is more than your 0.5 m/s target, so you’d need to use a bigger reduction or a smaller drum to drop the speed.

Integration with Linear Actuator Systems

When you couple rotary motors to lead screws or ball screws, the screw pitch ties the RPM directly to linear movement. For a given RPM N and screw pitch P (in mm per revolution), linear velocity (mm/s) = (N × P) ÷ 60. This is a key calculation if you want to make sure your setup can actually move fast enough for the task.

Advanced Considerations

If you’re working in the precision end of things, mechanical play, deflection, and even temperature changes can throw off the math a bit—closed-loop feedback can help if you need tight control. VFDs (variable frequency drives) let you dial in RPM on the fly, which means real-time adjustment of your linear output, but only if your calculations tie everything together correctly. Watch out for vibration issues, resonance, and centrifugal effects at high speed—these can sneak up on you well before you hit the limits of your components just by the math.

Frequently Asked Questions

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