Angular Acceleration Converter
Convert between rad/s², deg/s², rpm/s, and other angular acceleration units.
Angular Acceleration Converter
Enter an angular acceleration and select its unit — all others update instantly with visual gauges.
31.42 rad/s²
= 31.4159 rad/s²
= 1800 °/s²
Magnitude Comparison (rad/s²)
Quick References
How to Convert Between Rad/s², RPM/s, and Hz/s
A motor controller expects the ramp-up rate in rad/s², but your sensor outputs RPM/s. A conveyor motor programmed to reach 1,800 RPM in 3 seconds accelerates at 600 RPM/s. Type 600, select RPM/s, and see that it equals 62.83 rad/s², 10 Hz/s, and 22,619 deg/s². The tachometer gauge and bar chart show how this compares to real-world rotational accelerations.
The converter handles 5 units: rad/s², deg/s², rev/s² (same as Hz/s), RPM/s, and Hz/s. A robotics engineer programming a pick-and-place arm at 500 rad/s² sees it equals 4,775 RPM/s and 79.58 Hz/s. A physics student measuring a disk accelerating from rest to 600 RPM in 2 seconds enters 300 RPM/s and sees 31.42 rad/s² for the torque calculation τ = Iα.
When the wrong unit breaks your control loop
A variable frequency drive is programmed with a ramp rate of 600 RPM/s. The control engineer needs rad/s² for the torque equation. 600 RPM/s = 62.83 rad/s². If the engineer enters 600 directly into a formula expecting rad/s², the calculated torque is 9.55x too large, and the motor oversizes by the same factor. The converter eliminates this error.
A hard drive platter accelerates from 0 to 7,200 RPM in 0.5 seconds. That is 14,400 RPM/s = 240 Hz/s = 1,508 rad/s². The spin-up controller uses Hz/s to time the read/write head activation. If the head activates before the platter reaches speed, data corruption occurs. The converter helps verify the exact spin-up rate.
A collaborative robot arm has a maximum joint acceleration of 50 rad/s² for safety. The motor datasheet specifies torque in N·m and expects α in rad/s². If you accidentally use deg/s² (50 deg/s² = 0.873 rad/s²), the robot moves 57x slower than intended. If you use RPM/s (50 RPM/s = 5.24 rad/s²), the robot exceeds safety limits by 10x.
How the Angular Acceleration Converter Handles Rad/s² and RPM/s
All conversions pass through radians per second squared (rad/s²). When you enter 600 RPM/s, the tool multiplies by (2π)/60 = π/30 = 0.10472 to get 62.83 rad/s². Then it divides by each target unit's factor: by π/180 for deg/s², by 2π for Hz/s, by 1 for rad/s². The result: 600 RPM/s = 62.83 rad/s² = 3,600 deg/s² = 10 Hz/s.
Why RPM/s and rad/s² differ by a factor of 9.55
One revolution equals 2π radians (6.28319). RPM/s counts full revolutions per second per second. rad/s² counts radians per second per second. The conversion factor is 2π/60 = 0.10472 for RPM/s to rad/s², or equivalently 60/(2π) = 9.5493 for rad/s² to RPM/s. This factor is irrational (involving π), so it is stored as an IEEE 754 double-precision approximation with 15-17 significant digits.
The tachometer gauge and how it scales
The SVG tachometer shows your value on a semicircular arc. The needle position is proportional to your value relative to the maximum reference (jet turbine at ~5,000 rad/s²). The arc uses stroke-dasharray to show filled and unfilled portions. If your value exceeds the maximum reference, the needle pins to the right. If your value is very small, the needle stays near the left.
The bar chart below the gauge compares your value to 6 reference accelerations: turntable start-up (2 rad/s²), blender (50 rad/s²), car engine (209 rad/s²), hard drive (1,508 rad/s²), centrifuge (5,236 rad/s²), and jet turbine (20,944 rad/s²). Each bar scales linearly. Your bar is highlighted in blue while references are grey. This gives immediate visual context for whether your angular acceleration is modest or extreme.
Frequently Asked Questions
How do I convert 2000 RPM/s to rad/s²?
Multiply by π/30 (approximately 0.10472): 2000 x 0.10472 = 209.44 rad/s². This is the rate at which a car engine accelerates from idle to redline in about 3 seconds. For Hz/s, divide by 60: 2000 / 60 = 33.33 Hz/s. The converter shows all units simultaneously so you can verify the relationships.
What is the angular acceleration of a hard drive spin-up?
A typical 7,200 RPM hard drive reaches full speed in about 0.5 seconds. That is 14,400 RPM/s = 240 Hz/s = 1,508 rad/s². A 10,000 RPM drive spinning up in 0.8 seconds achieves 12,500 RPM/s = 208.3 Hz/s = 1,309 rad/s². The spin-up controller must time the read/write head activation precisely to avoid data corruption.
Why does the formula τ = Iα require rad/s²?
Newton's second law for rotation (τ = Iα) only works when α is in rad/s² because the radian is a dimensionless ratio. If you use RPM/s or deg/s², you get wrong torque values. For example: I = 2 kg·m², α = 600 RPM/s. The correct torque is τ = 2 x 62.83 = 125.66 N·m. Using 600 directly gives τ = 1200 N·m, which is 9.55x too large.
How is angular acceleration different from angular velocity?
Angular velocity (ω) measures how fast something rotates (rad/s). Angular acceleration (α) measures how fast the rotation speed changes (rad/s²). A motor running at constant 3000 RPM has ω = 314.16 rad/s but α = 0. If it speeds up from 0 to 3000 RPM in 2 seconds, α = 157.08 rad/s². Acceleration is the derivative of velocity.
What is a realistic angular acceleration for a car engine?
A typical car engine accelerates from idle (1,000 RPM) to redline (7,000 RPM) in about 3 seconds. That is 2,000 RPM/s = 209.44 rad/s² = 33.33 Hz/s. A high-performance engine might do this in 1.5 seconds: 4,000 RPM/s = 418.88 rad/s². Formula 1 engines reach 18,000 RPM from idle in under 0.5 seconds: over 30,000 RPM/s.
How do I measure angular acceleration experimentally?
Use a rotary motion sensor connected to a data logger. Record angular position or velocity over time. Compute α = Δω / Δt from the slope of the velocity-time graph. If a disk goes from 0 to 600 RPM in 2 seconds, the average α is 300 RPM/s = 31.42 rad/s². For instantaneous α, take the derivative of the velocity curve at each point.