Drilling Thrust and Torque Formulas

Drilling thrust and torque are different loads. Thrust acts along the drill axis as the tool advances; torque is the twisting moment needed to rotate the cutting edges. The equations below collect selected metric relationships from a tooling-manufacturer reference so engineers can check units and understand dependencies. They are estimates, not a universal force chart or a recommendation for a specific drill, material or machine. Use the tool maker’s data and the machine’s rated limits for the actual setup.

Drilling Thrust and Torque Factors

MECHANITEC / ENGINEERING REFERENCE

Drilling thrust, torque and power formulas

Selected metric manufacturer formulas and symbol definitions for estimating common drilling quantities. Formula outputs depend on the chosen cutting data and tool geometry.

1–6 of 6 matching rows (6 total)

Drilling thrust, torque and power formulas — page 1 of 1
Calculation	Symbol	Formula	Result unit	Input definitions	Scope note
Penetration rate	vf	vf = fn × n	mm/min	fn: feed per revolution (mm/rev); n: spindle speed (rev/min).	Kinematic conversion; does not choose a feed value.
Spindle speed	n	n = vc × 1000 / (π × Dc)	rev/min	vc: cutting speed (m/min); Dc: drill diameter (mm).	Use diameter at the cutting edge; final machine setting is constrained by tooling and machine limits.
Estimated net cutting power	Pc	Pc = vc × Dc × fn × kc / 240000	kW	vc: m/min; Dc: mm; fn: mm/rev; kc: specific cutting force (N/mm²).	Manufacturer model estimate; kc depends on work material and chip conditions.
Torque from net power	Mc	Mc = Pc × 30000 / (π × n)	N·m	Pc: kW; n: rev/min. n must be nonzero.	Power-based relationship; low-speed torque limits and drive efficiency require separate machine data.
Estimated drilling feed force	Ff	Ff ≈ 0.5 × kc × (Dc / 2) × fn × sin(KAPR)	N	kc: N/mm²; Dc: mm; fn: mm/rev; KAPR: entering angle in degrees.	Approximate cutting-edge estimate. Chisel-edge thrust, drill geometry, wear and material condition can materially change actual force.
Metal removal rate	Q	Q = vc × Dc × fn / 4	cm³/min	vc: m/min; Dc: mm; fn: mm/rev.	Ideal full-circular drilling estimate; use the tool maker’s method for step, interrupted or specialized drilling.

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Inputs and formula relationships

The symbols Dc, fn and vc represent drill diameter, feed per revolution and cutting speed. The specific cutting force kc describes the work material’s resistance in the selected cutting model. Feed rate vf follows from feed per revolution times spindle speed. Spindle speed can be derived from cutting speed and drill diameter. These conversions establish the operating point, but they do not choose a safe or productive value for cutting speed or feed.

Net cutting power is estimated from cutting speed, drill diameter, feed per revolution and specific cutting force. Torque can then be related to power and rotational speed. Because torque is power divided by angular speed, the same power implies higher torque at lower speed. When using the equation, keep Pc in kilowatts and n in revolutions per minute to obtain Mc in newton-metres. The formula requires n greater than zero; it is not a way to estimate static holding torque at standstill.

The feed-force expression is approximate and depends on kc, drill diameter, feed and the entering angle. It describes a simplified cutting-edge estimate. Actual thrust includes contributions from the chisel edge and changes with point geometry, web thickness, lip condition, drill wear, material hardness, chip evacuation and coolant. The table intentionally labels it an estimate rather than a rated or measured force.

Worked example: torque from power

Assume a calculation estimates 2.0 kW net cutting power at 1,000 rev/min. Torque is Mc = 2.0 × 30,000 / (π × 1,000), or about 19.1 N·m. If speed falls while required cutting power remains the same, the calculated torque rises. This example only demonstrates the power-speed relationship; it is not a recommendation to use 2.0 kW or 1,000 rpm for an unspecified tool and material.

As a separate unit check, a 10 mm drill at 100 m/min has a calculated spindle speed of about 3,183 rev/min using n = vc × 1000 / (π × Dc). With a feed of 0.1 mm/rev, the corresponding penetration rate is about 318 mm/min. The correct machining feed may be very different depending on the drill diameter, material group, drill type, hole depth and manufacturer’s recommendation.

How to apply thrust and torque estimates

Compare the predicted thrust with fixture, toolholder, spindle and workholding capabilities, and compare torque and power with the machine’s capability at the chosen rpm. A machine’s maximum power may only be available over part of its speed range. Also account for drive efficiency, torque curves, spindle taper, tool overhang, coolant delivery and chip evacuation. Interrupted cuts, angled entry, cross holes and breakthrough can produce transient loads that a simple steady-state formula does not capture.

Material condition matters. A generic kc value is not universal for every alloy, hardness, heat treatment or chip thickness. Use the current tooling recommendation for the exact material and drill geometry. When a force value is safety-critical, validate it with the manufacturer’s calculator or documented test data rather than treating a simplified formula as a certified machine load.

Limits

Thrust cannot be inferred from torque alone, and neither value establishes tool life, hole quality or structural safety. The equations assume consistent units and a simplified operation. Confirm the exact model definitions, tool geometry and input conventions in the cited source. Stop and investigate if measured load differs sharply from expectation; a dull drill, poor alignment, packed chips or workpiece movement may be involved.

Source

Formula relationships are adapted from Sandvik Coromant’s metric drilling formulas and definitions. Use the drill manufacturer’s current recommendations and machine documentation for application-specific limits.