Tools / Physics
Angular Acceleration Calculator
Angular acceleration calculator — compute α from Δω/Δt or τ/I, missing-variable solver, and unit conversion. SI unit: rad/s².
α from angular velocity change & time
α = (ωf − ωi) / Δt
α from torque & moment of inertia
α = τ / I
Solver — find the missing variable
α = (ωf − ωi) / t
Angular acceleration unit conversion
Results
α—
α—
α—
at—
Verified examples
- Δω/Δt mode: ω 0 → 3,600 rpm in 10 s ⇒ α = 37.69911184 rad/s² = 360 rpm/s = 2,160 deg/s².
- τ/I mode: τ = 50 N·m, I = 10 kg·m² ⇒ α = 5 rad/s² = 286.4788976 deg/s².
- Solver: ωi = 10 rpm, α = 2 rad/s², t = 8 s ⇒ ωf = 17.04719755 rad/s = 162.7887454 rpm.
- Tangential: α = 5 rad/s² at radius 0.3 m ⇒ at = 1.5 m/s².
Note: the numbers above were recomputed from this calculator's engine, not from memory.
Methodology
Angular acceleration α is the rate of change of angular velocity ω over time; its SI unit is radians per second squared (rad/s²). Conversion uses exact definitions: 1 revolution = 2π radians, 1 minute = 60 seconds, 1 revolution = 360°.
- 1 rad/s² = 57.29577951 deg/s² = 9.549296586 rpm/s.
- 60 rpm = 2π rad/s ≈ 6.28318531 rad/s.
- Newton's law of rotational motion: τ = I·α, so α = τ/I for known torque and moment of inertia.
- Distinguish angular acceleration α (rad/s²) from tangential acceleration at = α·r (m/s²) — the linear acceleration of a point at distance r from the rotation axis. This calculator shows it when a radius is entered.
Scope limits
This tool is specifically for angular acceleration. For linear frequency and static angular velocity, use frequency-converter (Hz ↔ rpm ↔ rad/s, including the ω↔f tab) — that one does not compute acceleration. For Hz ↔ rad/s conversion only, see hz-to-rads. This tool does not compute bolt torque (see bolt-torque) or motor torque (see electric-motor-torque) — here torque is only an input for α = τ/I.
FAQ
What is angular acceleration?
Angular acceleration (α) is how fast angular velocity ω changes over time, measured in rad/s² (SI). Example: a motor reaching 3,600 rpm from rest in 10 seconds experiences α = 37.69911184 rad/s².
How do you compute angular acceleration from rpm and time?
α = (ωf − ωi) / Δt. First convert rpm to rad/s (multiply by 2π/60 ≈ 0.10471975512). Example: 0 → 3,600 rpm in 10 s ⇒ Δω = 376.99111843 rad/s ⇒ α = 37.69911184 rad/s² = 360 rpm/s.
How do you compute angular acceleration from torque and moment of inertia?
Use α = τ/I. Example: 50 N·m torque with 10 kg·m² moment of inertia ⇒ α = 5 rad/s² (or 286.4788976 deg/s²).
What is the difference between angular and tangential acceleration?
Angular acceleration α (rad/s²) measures the change in rotation rate; tangential acceleration at = α·r (m/s²) is the linear acceleration of a point at distance r from the axis. Example: α = 5 rad/s² at r = 0.3 m ⇒ at = 1.5 m/s².
How much is 1 rad/s² in deg/s² and rpm/s?
1 rad/s² = 57.29577951 deg/s² = 9.549296586 rpm/s (from 1 rad = 180/π degrees and 1 minute = 60 seconds).
Why does the calculator reject time = 0?
Because α = Δω/Δt; division by zero is undefined. An instantaneous change in angular velocity (Δt = 0) physically means infinite acceleration, which cannot be computed — enter a valid duration.
Is this tool the same as frequency-converter?
No. frequency-converter converts static frequency/angular velocity (Hz, rpm, rad/s) without a rate-of-change dimension; this tool computes its rate of change (angular acceleration) from Δω/Δt or τ/I.
What is the SI unit of angular acceleration?
Radians per second squared (rad/s²). This calculator shows rad/s² as the primary result, plus rpm/s and deg/s² for practical needs.
Free tool by NRTechStudio