Estimate the first critical speed of a rotating shaft using shaft deflection, geometry, material, and operating RPM. Use this for conveyor rollers, drive shafts, long unsupported shafts, pulleys, sprockets, spindles, and rotating machine components.
Use either the quick deflection method or calculate shaft deflection from a supported shaft load case. The calculator estimates first critical speed and compares it to operating RPM.
Shaft critical speed is the RPM where a rotating shaft can begin to whirl or resonate. Running too close to critical speed can create vibration, noise, bearing damage, seal issues, belt tracking problems, and fatigue failures.
It is not a torque limit or a horsepower limit. A shaft can have enough torque capacity and still vibrate badly if it runs near its critical speed.
The simple critical-speed estimate is based on static deflection. Less deflection usually means higher critical speed.
For practical machine design, avoid operating near the calculated critical speed. The calculator uses a separation target to help flag risky speeds.
This calculator uses a practical first-mode estimate based on static deflection. It is useful for early design checks, but real shafts may need detailed rotordynamic review.
Approximate First Critical Speed:
Ncritical ≈ 187.7 / √δ
Where:
Ncritical = critical speed in RPM
δ = static deflection in inches
Metric conversion used:
δ(in) = δ(mm) / 25.4
Solid Round Shaft:
I = πd⁴ / 64
Hollow Round Shaft:
I = π(OD⁴ - ID⁴) / 64
Center Point Load Deflection:
δ = P × L³ / (48 × E × I)
Uniform Load Deflection:
δ = 5 × w × L⁴ / (384 × E × I)
Overhung End Load Deflection:
δ = P × a³ / (3 × E × I)
Do not check critical speed by itself. A rotating shaft also needs checks for deflection, bearing loading, torque, alignment, and operating duty.
Deflection is the best first signal. If the shaft bends too much, the critical speed will usually be lower and the bearings may see poor loading.
Use the separation margin to decide whether the shaft is comfortably below critical speed or too close for a practical machine design.
A shaft running near a vibration condition can damage bearings even when the static load rating looks acceptable.
If the shaft is part of a conveyor, gearbox, pulley, or servo-driven axis, check motion speed and torque after the shaft stiffness looks reasonable.
If operating speed is too close to critical speed, the most effective fixes usually change stiffness, span, support location, or operating RPM.
Critical speed is one part of rotating shaft design. Use these related tools to check the rest of the system.
Estimate shaft deflection from bearing span, load, diameter, and material stiffness.
Open Shaft Deflection →Check bearing life when shaft loads and vibration may reduce service life.
Open Bearing Life →Convert roller diameter and RPM into conveyor speed for rotating shaft systems.
Open Conveyor Speed →Check output torque when the shaft is driven by a gearbox or reducer.
Open Gearbox Torque →Calculate speed reduction, output RPM, and torque relationship for driven shafts.
Open Gear Ratio →Return to the full workflow for structures, shafts, bearings, motion, and fastening.
Open Machine Design Hub →If the margin is tight, improve shaft stiffness, shorten the span, reduce overhung load, lower RPM, or get the rotating assembly reviewed before it becomes a vibration problem.