Lathe and Mill Speeds and Feeds Calculator: RPM and Power
Calculate lathe or mill RPM, feed, metal removal, cutting power and torque. Compare machine limits using HSS/carbide starting speeds and chip-thickness-corrected cutting force.
This lathe RPM calculator and speeds and feeds calculator connects cutting speed, spindle speed, feed, metal removal and machine load. It is intended for engineers planning a metal-cutting pass, students checking machining calculations, and workshop users comparing a proposed cut with their machine. Choose longitudinal turning or a straight peripheral milling cut, including full-width slotting.
Start with the workpiece material and tool material. The HSS and carbide speed presets are published starting values for annealed 4140-type steel, wrought aged aluminium and free-cutting brass. They are not a complete cutting-data recommendation: coating, hardness, insert geometry, coolant, rigidity and tool life all matter. The turning preset source assumes a light cut. Replace the preset with your tool maker's cutting speed whenever that information is available, or enter the RPM of an actual gear or belt setting.
For turning, enter the mean diameter of the layer being removed, radial depth of cut and feed per revolution. The stock diameter is a useful approximation for a shallow pass. For milling, enter effective cutter diameter, axial depth, radial width and effective teeth per revolution. Enter either advance per tooth or a known table feed. Length units on the advance fields mean distance per revolution or per tooth, as their labels state. The unit switch converts dimensions, advance per revolution or tooth, power and torque. In the current viewer, cutting speed stays in m/min, linear feed in mm/min, metal removal in cm³/min and the kc result in N/mm². Read each unit: charts can also use mixed units in US mode.
The calculator caps the requested spindle speed at the permitted maximum and uses that capped speed throughout. With advance per revolution or tooth selected, the linear feed decreases with RPM. With a linear feed entered, that feed stays fixed and chip thickness increases when RPM falls. Always inspect the actual cutting speed and advance after a cap applies.
As a milling power calculator, it estimates specific cutting force from a material constant and mean uncut chip thickness. Thinner chips require more energy per unit volume in this empirical model. Your own kc1 and chip-thickness exponent, or a known effective kc, can instead be entered. Net cutting power is the mechanical power at the cutting edge; required drive power includes the entered transmission efficiency. Compare power and mean torque independently using continuous machine ratings at the selected RPM.
The chart varies feed at fixed RPM and geometry. Its limit line includes both available power and the entered torque limit; it does not certify a stable cut. Tune starting values on the machine while observing chip evacuation, vibration, spindle load and finish. This tool excludes chatter prediction, tool deflection, peak tooth loads, tool-life optimisation, ball-nose and high-feed cutters, centred face milling, drilling, tapping, facing with changing diameter, and complete cycle-time estimation. The separate CNC Router calculator covers router-oriented wood and aluminium work.
How it is calculated
The speed, feed, removal-rate, power and torque relationships follow Sandvik Coromant's turning formulas (https://www.sandvik.coromant.com/en-gb/knowledge/machining-formulas-definitions/general-turning-formulas-definitions) and milling formulas (https://www.sandvik.coromant.com/en-gb/knowledge/machining-formulas-definitions/milling-formulas-definitions). Each conversion is explicit in the calculation steps.
For Vc in m/min and D in mm, n = 1000 Vc/(Ï€D). The actual speed is the smaller of requested RPM and maximum permitted RPM. Actual Vc is recalculated from this speed. Linear feed is fn n in turning and fz z n in milling, unless the user supplies a linear feed directly.
Turning uses Q = Vc ap fn in cm³/min. D is the mean diameter of the removed annulus: with outer diameter Do, use D = Do − ap. This makes the volume identity exact for a cylindrical longitudinal pass. Using Do as D approximates a shallow pass. Milling uses Q = ap ae vf/1000 in cm³/min.
The specific-force model is kc = kc1 (hm/1 mm)^(−mc) (1 − γ/100), with γ in degrees. This form is given in Sandvik's HRSA Application Guide, printed p.119 (https://cdn.sandvik.coromant.com/files/sitecollectiondocuments/downloads/global/technical%20guides/en-gb/c-2920-034.pdf) and ISCAR's Cutting Tools User Guide, printed p.55. The reference thickness is explicitly 1 mm; changing display units never changes this calibration. Steel coefficients are from Sandvik 18.2, attached source s2, PDF p.72 (printed A70); brass coefficients are from the 2017 supplement, printed A40. Aluminium uses the matched ISCAR Material Groups class 22 pair: kc1 = 800 N/mm², mc = 0.25 at 100 HB (one-page source (https://www.iscar.com/lms/wp-content/uploads/2021/04/Materials-group.pdf)). All are material-class estimates rather than values certified for a particular heat. The custom-coefficient option uses the user's kc1 and mc at the same 1 mm, zero-rake reference.
Turning hm = fn sin(KAPR). For a straight 90° peripheral milling cut from a free edge, this tool derives the engaged arc β = acos(1 − 2ae/D), in radians. Integrating the small-feed geometry h(φ) = fz sin φ from 0 to β gives hm = fz(1 − cos β)/β = 2fz ae/(Dβ). This is an arc average for side milling; the centred face-milling geometry in the Sandvik guide is different. Maximum chip thickness is fz sin β for ae < D/2 and fz otherwise. No automatic feed compensation is applied.
Power at the cut is kc times volume per second, converted to kW. Required drive power is Pcut/η. Spindle torque is Pcut/ω, with ω = 2πn/60. Available spindle power is η Pdrive; the chart's effective power limit is min(η Pdrive, Tlimit ω). At fixed RPM, corrected-model power varies with feed^(1 − mc), while fixed-kc power varies directly with feed. Pass time is cutting length divided by linear feed.
Assumptions
- Steady longitudinal turning or a straight 90° peripheral milling pass. A full slot is allowed. Milling assumes an undeformed chip small compared with cutter diameter and uniform effective teeth.
- Turning diameter is the mean diameter of the removed layer, not a CSS simulation. Depth is radial in turning and axial in milling.
- Specific cutting force at mean chip thickness approximates mean power. It does not resolve individual teeth, helix, edge forces, tool wear or runout. Tool-specific data supersede the class values.
- Starting speeds come from LittleMachineShop turning data (lower endpoints where a range is given) and CIMCO prototype milling Table 3.5. The aluminium carbide turning value is high and may be RPM-limited. Feeds are user inputs, not material recommendations.
- Enter mechanical drive power available continuously before spindle losses; set efficiency to 1 for a spindle-output power rating. Torque is the continuous spindle value at the selected RPM and is independent of the motor power entry.
- Chart sweeps retain RPM, engagement, geometry, rake, efficiency and the entered torque limit. A new RPM requires a fresh torque-curve reading.
- This is a static sizing calculation. The schematic exaggerates chip thickness and depth for legibility.
Where it applies
Use for initial estimates in ordinary metal cutting, then tune on the machine with tool-maker guidance. The included material classes are non-hardened low-alloy steel near 175 HB, wrought aged aluminium near 100 HB, and free-cutting brass near 110 HB; a different heat or hardness can change force materially. For another material, enter kc1 and mc from a matched source, or supply an effective kc, together with a custom speed or RPM.
Milling radial width must not exceed cutter diameter. Turning radial depth must be less than mean cutting diameter to leave a positive inner diameter. The force-model warnings below 0.01 mm and above 1.5 mm mean chip thickness are screening limits chosen here, not manufacturer tool limits. The feed/diameter warning above 0.05 similarly flags the small-feed approximation.
Do not use these results as a chatter limit, a peak cutting-force prediction, a spindle bearing-load check, or a guarantee of tool life or finish. Centred face milling, round inserts, ball-nose tools, high-feed geometry, ploughing-dominated micromachining and rapidly changing engagement need their own models. Pass time excludes acceleration, positioning, tool changes and interruptions. Neither power nor torque checks establish acceptable workholding.
Reference cases include Mitsubishi's worked turning feed and milling power examples. The milling source uses π = 3.14 (101.91 RPM); full π gives 101.859 RPM. Its stated 0.228 mm/tooth is a truncation/inconsistency: 280/(12 × 101.859) = 0.229074 mm/tooth. The published 1.68 kW includes 80% efficiency; the corresponding net cut power is 1.344 kW. The calculation retains those conventions without altering the formulas.
The ISCAR worked force example, printed p.55, gives kc = 3745 N/mm² for kc1 = 2450 N/mm², mc = 0.23, hm = 0.1 mm and 10° rake. This provides a separate check of the nontrivial chip-thickness and rake corrections.
Display units: the current viewer's global US switch converts lengths, power and torque but has no automatic mapping for m/min, mm/min, cm³/min or N/mm². These rate and specific-force result cards retain their metric units. The feed-power chart therefore keeps mm/min on its horizontal axis while power changes to hp. The specific-force chart uses mm and MPa in metric mode, and in and ksi in US mode. Follow each printed axis and result unit.
References
- Sandvik Coromant, Turning formulas and definitions. https://www.sandvik.coromant.com/en-gb/knowledge/machining-formulas-definitions/general-turning-formulas-definitions
- Sandvik Coromant, Milling formulas and definitions. https://www.sandvik.coromant.com/en-gb/knowledge/machining-formulas-definitions/milling-formulas-definitions
- Sandvik Coromant, Heat resistant super alloys application guide, printed p.119: force and power model. https://cdn.sandvik.coromant.com/files/sitecollectiondocuments/downloads/global/technical%20guides/en-gb/c-2920-034.pdf
- Sandvik Coromant 18.2 supplement, PDF p.72 / printed A70, low-alloy steel force constants (attached s2). https://www.sktools.sk/wp-content/uploads/2018/10/cp-18-2-supplement-eng.pdf
- Sandvik Coromant 2017 supplement, printed A40, free-cutting brass force constants. https://cdn.dgisupply.com/img/product-images/Asset_URL/Sandvik_Coromant_7379294_Catalog.pdf
- LittleMachineShop, Cutting Speeds: turning HSS and carbide rows. https://littlemachineshop.com/pages/cutting-speeds
- CIMCO CNC Handbook, Cutting Data, Table 3.5: prototype milling speeds. https://docs.cimco.com/en/docs/cnc-handbook/1/cnc-tools/cutting-data/
- Mitsubishi Materials, Basic Turning: Formulas, worked feed example. https://www.mmc-carbide.com/permanent/courses/85/formulas.html
- Mitsubishi Materials, Cutting Power for Face Milling: worked 1.68 kW example; used here to verify speed, removal and fixed-kc power, not peripheral chip geometry. https://www.mmc-carbide.com/sea/technical_information/formula/tec_milling_power_formula
- ISCAR, Cutting Tools User Guide, printed p.55, specific cutting-force model. https://www.iscar.se/Catalogs/Publication/Reference_Guide/english_1/Cutting_tools_user_guide/Cutting_tools_user_guide.pdf
- ISCAR, Material Groups, one-page PDF, material 22: hardenable wrought aluminium, kc1=800 N/mm², mc=0.25, 100 HB. https://www.iscar.com/lms/wp-content/uploads/2021/04/Materials-group.pdf
Inputs
| Input | Symbol | Unit | Default |
|---|---|---|---|
| Operation | operation | Lathe turning | |
| Specific cutting force model Material presets supply kc1 and mc. Use your own coefficients for another material, or enter an effective kc already corrected for this cut. | force_mode | Material kc1 + mc | |
| Set spindle speed from | speed_mode | Material preset | |
| Workpiece material Condition and approximate Brinell hardness (HB) describe the selected material class. Verify the actual heat and hardness. | stock | 4140 steel | |
| Cutting tool material | tool_grade | Carbide | |
| Target cutting speed | V_custom | m/min | 150 |
| Machine speed setting Use this for a gear/belt speed or the RPM you intend to program. The maximum RPM still applies. | n_set | rpm | 1000 |
| Cutting diameter, Dcut Turning: mean removed-layer diameter, Dcut = Dₒ − ap, where Dₒ is outside stock diameter. Milling: effective cutter diameter at the cut. | D_cut | mm | 50 |
| Depth of cut Turning: radial depth (diameter reduces by twice this). Milling: axial depth. | a_p | mm | 2 |
| Milling radial width of cut Straight side cut from a free edge; set equal to cutter diameter for a full slot. Centred face milling uses different chip geometry. | a_e | mm | 20 |
| Effective teeth per revolution Number of teeth that each cut the same track once per turn; not the instantaneous number engaged. | z_teeth | 4 | |
| Enter feed as Lathe: distance per revolution. Mill: distance per tooth. Linear feed is distance per minute. | feed_mode | Per rev / tooth | |
| Turning feed per revolution Length advanced in one spindle revolution (mm/rev or in/rev). Select from the insert or tool maker's data. | f_turn | mm | 0.2 |
| Milling feed per tooth Length advanced per effective tooth (mm/tooth or in/tooth). No automatic chip-thinning feed increase is applied. | f_tooth | mm | 0.1 |
| Linear cutting feed The entered feed is retained if the RPM cap applies; inspect the resulting feed per revolution or tooth. | v_enter | mm/min | 280 |
| Length of one cutting pass Used for cutting time only. Include approach travel yourself; acceleration, rapids and tool changes are excluded. | L_cut | mm | 100 |
| Turning entering angle KAPR, measured between the main cutting edge and feed direction. Milling assumes a 90° shoulder. | K_enter | deg | 90 |
| Effective rake angle A positive rake reduces estimated specific cutting force. The empirical correction is 1 − rake/100 with rake expressed in degrees. | gamma_r | deg | 0 |
| My specific cutting force at 1 mm chip kc1 referenced to 1 mm uncut chip thickness and zero rake, not an effective kc at another feed. | k_user | N/mm^2 | 2450 |
| My chip-thickness exponent Dimensionless exponent mc from the same material data as kc1. | m_user | 0.23 | |
| Known effective specific cutting force Use an effective kc already matched to this chip thickness and tool geometry. The chip-thickness and rake corrections are bypassed. | k_known | N/mm^2 | 1800 |
| Maximum permitted spindle speed Use the lowest permitted speed limit of machine, chuck, tool and workholding. | n_max | rpm | 3000 |
| Available continuous drive power Mechanical motor power available before transmission losses, not wall electrical input. If using a spindle-output rating, set efficiency to 1. | P_drive | kW | 5.5 |
| Drive-to-spindle efficiency Fraction, 0.85 = 85%. Use 1 when the power rating is already measured at the spindle. | eta_drive | 0.85 | |
| Available spindle torque at this RPM Continuous spindle torque available at the calculated speed. Read the machine's torque curve and update when changing speed. | T_limit | N*m | 40 |
Results
With the default inputs above, the calc gives:
| Result | Value |
|---|---|
| Spindle speed to use | 834 1/min |
| Actual cutting speed | 131.1 m/min |
| Linear feed rate | 166.9 mm/min |
| Advance per revolution | 0.2 mm |
| Advance per cutting edge | 0.2 mm |
| Metal removal rate | 52.43 cm³/min |
| Mean uncut chip thickness | 0.2 mm |
| Effective specific cutting force | 2,542 N/mm² |
| Net cutting power | 2.221 kW |
| Required drive power | 2.613 kW |
| Mean spindle cutting torque | 25.42 N·m |
| Power capacity used (1 = full) | 0.475 |
| Torque capacity used (1 = full) | 0.636 |
| Cutting time per pass | 0.599 min |
Checked against sources
Each case below was calculated by this calc and agrees with the value from its source (within the tolerance where one is shown).
Mitsubishi turning: 100 mm in one minute
Source: Mitsubishi Materials, Basic Turning — Formulas: 10 mm shaft, 100 mm length in 1 minute at 1,000 RPM, cutting feed 100 mm/min. The implied advance is 0.1 mm/rev. https://www.mmc-carbide.com/permanent/courses/85/formulas.html
Inputs: Set spindle speed from = Machine RPM; Cutting diameter, Dcut = 10 mm; Depth of cut = 1 mm; Turning feed per revolution = 0.1 mm; Specific cutting force model = Known kc; the others as above.
| Result | Source | This calc |
|---|---|---|
| Spindle speed to use | 1,000 1/min | 1,000 1/min |
| Linear feed rate | 100 mm/min | 100 mm/min |
| Cutting time per pass | 1 min | 1 min |
Mitsubishi milling: 1.68 kW drive demand
Source: Mitsubishi Materials, Cutting Power for Face Milling, Example: Vc=80 m/min, D=250 mm, ap=2 mm, ae=80 mm, vf=280 mm/min, z=12, effective kc=1800 MPa and efficiency=0.8; published drive demand 1.68 kW. Removal 44.8 cm³/min is the source's 2×80×280 numerator converted to volume units. Its 101.91 RPM uses π=3.14; full π gives 101.859. Published fz=0.228 is inconsistent with its inputs (0.229074 here) and is not forced into the model. This case checks fixed-kc power, not the face-milling chip shape. https://www.mmc-carbide.com/sea/technical_information/formula/tec_milling_power_formula
Inputs: Operation = Peripheral milling; Set spindle speed from = Cutting speed; Target cutting speed = 80 m/min; Cutting diameter, Dcut = 250 mm; Milling radial width of cut = 80 mm; Effective teeth per revolution = 12; Enter feed as = Linear feed; Specific cutting force model = Known kc; Drive-to-spindle efficiency = 0.8; Available continuous drive power = 10 kW; Available spindle torque at this RPM = 200 N·m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Spindle speed to use | 101.9 1/min | 101.9 1/min |
| Metal removal rate | 44.8 cm³/min | 44.8 cm³/min |
| Required drive power | 1.68 kW | 1.68 kW |
Sandvik low-alloy steel: 1 mm reference chip
Source: Sandvik Coromant 18.2 supplement, attached PDF p.72 (printed A70), material class 02.1 non-hardened low-alloy steel: kc1=1700 N/mm² at a 1 mm chip, 175 HB, mc=0.25. The model must recover this independently published calibration point at zero rake. https://www.sktools.sk/wp-content/uploads/2018/10/cp-18-2-supplement-eng.pdf
Inputs: Set spindle speed from = Cutting speed; Target cutting speed = 100 m/min; Depth of cut = 1 mm; Turning feed per revolution = 1 mm; Available continuous drive power = 100 kW; Available spindle torque at this RPM = 500 N·m; the others as above.
| Result | Source | This calc |
|---|---|---|
| Mean uncut chip thickness | 1 mm | 1 mm |
| Effective specific cutting force | 1,700 N/mm² | 1,700 N/mm² |
| Material chip-thickness exponent | 0.25 | 0.25 |
ISCAR: thin-chip and rake correction
Source: ISCAR Cutting Tools User Guide, printed p.55, equations 8.6–8.7: worked example kc=2450×0.1^(−0.23)×(1−0.1)=3745 N/mm². Published result is rounded. This independently published example exercises both chip-thickness and rake corrections; kc1 and mc are user-supplied to match the example's tool-steel class, not the default preset. https://www.iscar.se/Catalogs/Publication/Reference_Guide/english_1/Cutting_tools_user_guide/Cutting_tools_user_guide.pdf
Inputs: Specific cutting force model = Enter kc1 + mc; Set spindle speed from = Cutting speed; Target cutting speed = 100 m/min; Depth of cut = 1 mm; Turning feed per revolution = 0.1 mm; Effective rake angle = 10 deg; the others as above.
| Result | Source | This calc |
|---|---|---|
| Effective specific cutting force | 3,745 N/mm² | 3,745 N/mm² |
ISCAR wrought aluminium: matched reference coefficients
Source: ISCAR Material Groups, one-page PDF (printed p.1112), hardenable wrought aluminium, material 22. Published row: "Hardenable 800 0.25 100 22". The pair is kc1=800 N/mm² and mc=0.25 at 100 HB. Zero rake and a 1 mm chip recover the independently published reference specific force. Both coefficients come from this same ISCAR row; Sandvik class 30.12's blank exponent is not filled by assumption. https://www.iscar.com/lms/wp-content/uploads/2021/04/Materials-group.pdf
Inputs: Workpiece material = 6061 aluminium; Set spindle speed from = Cutting speed; Target cutting speed = 100 m/min; Depth of cut = 1 mm; Turning feed per revolution = 1 mm; the others as above.
| Result | Source | This calc |
|---|---|---|
| Specific cutting force at 1 mm chip thickness | 800 N/mm² | 800 N/mm² |
| Material chip-thickness exponent | 0.25 | 0.25 |
| Effective specific cutting force | 800 N/mm² | 800 N/mm² |
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