Feed Rate Calculator
Compute table feed rate for milling, drilling and turning operations using fr = f · N — with three-way solving for feed rate, feed per revolution or spindle speed, a live tool-and-workpiece schematic, and companion cutting metrics including cutting speed, chip load per tooth and material removal rate.
Feed rate is the machine's translational speed
While the spindle speed N sets how fast the cutter spins, the feed rate fr sets how fast the workpiece moves past it. The two are linked by the chip load f: for every revolution of the cutter, the workpiece advances by exactly f millimetres, so the table must move at f · N millimetres per minute. This is the equation that couples tool geometry, spindle speed and machine motion — and it is why the same physical operation can be programmed with different combinations of f and N provided the product stays the same.
Chip load is the limiting variable, not feed rate
What actually determines whether a cut is safe or aggressive is the chip load per tooth, fz — the thickness of material each cutting edge engages per pass. Too small a chip load leads to rubbing, work-hardening and rapid tool wear. Too large a chip load overloads the tooth and can break it. Feed rate fr and spindle speed N are chosen to produce the correct fz for the material and tool. The relation fz = fr / (z · N) is therefore the design equation, and fr = f · N is simply its rearrangement.
Higher speed at the same chip load means higher feed
If you increase spindle speed N without changing the chip load per tooth, the feed rate must increase proportionally. This is the logic behind high-speed machining: run the spindle as fast as the tool and spindle bearings allow, and feed the table proportionally faster so that each tooth still bites the same small, consistent chip. The result is a much higher material removal rate at the same cutting forces and the same tool life per unit volume of material removed.
Exceeding the feed rate saturates the axis
Every machine has a maximum feed rate — the speed at which the servo axes can still track the commanded path without lag or overshoot. If the calculated fr exceeds this limit, the machine will either alarm, lag the contour, or interpolate incorrectly, producing a poor surface finish and dimensional errors. This is why high-speed machining centres have both a high spindle speed and a high axis feed capability — the two must scale together for the machining strategy to work at all.
How to Use This Calculator
The feed relation links three quantities: fr, f and N. Pick which one you want the tool to solve, then fill in the other two.
1. Choose what to solve for
Pick fr, f or N from the toggle. The calculator rearranges fr = f · N automatically for whichever variable you choose.
2. Choose your feed definition
Direct mode uses feed per revolution f. Milling mode lets you enter feed per tooth fz and number of teeth z, and the calculator computes f = fz · z automatically — the more natural way to specify a milling operation.
3. Use realistic presets
Presets cover typical values: feed rates from 10 to 8,000 mm/min, feeds per revolution from 0.02 to 2 mm/rev, and spindle speeds from 200 to 24,000 RPM. The milling presets cover 1 to 12 flutes.
4. Read the result and verdict
The result card shows the solved value plus equivalents in mm/s, m/min and in/min. A colour-coded verdict classifies the feed from very low through low, moderate, high, very high, high-speed and extreme.
5. Check the schematic and charts
The schematic shows a top-down view of the milling operation — the workpiece advancing at fr, the cutter rotating at N, and the chip load f marked between successive tooth engagements. The main chart plots fr against spindle speed for three feeds.
6. Switch to Advanced for depth
Advanced mode adds a fr vs. f chart, a sensitivity analysis, and companion metrics — cutting speed vc, chip load per tooth fz, material removal rate MRR, specific cutting power, and spindle torque estimate — all with an editable tool diameter, depth of cut ap and width of cut ae.
What This Tool Offers
Built around the classic machining relation fr = f · N, the fundamental link between feed per revolution, spindle speed and table feed.
Three-way solving
Solve for feed rate, feed per revolution, or spindle speed. The calculator rearranges the formula for whichever variable you choose.
Direct and milling modes
Enter feed per revolution directly, or switch to milling mode and enter feed per tooth fz and number of teeth z — the calculator handles f = fz · z automatically.
Live milling schematic
A top-down view of the workpiece advancing at fr, the rotating cutter with visible flutes and rotation arrow at N RPM, and the chip load f marked between successive teeth.
Feed-class verdict
Each result is classified from very low through low, moderate, high, very high, high-speed and extreme, with a coloured badge and a reference to the typical machining regime.
Companion cutting metrics
Cutting speed vc, chip load per tooth fz, feed per tooth in inches, material removal rate MRR, and spindle torque estimate — all live in advanced mode.
Reference tables
A feed rate lookup grid, a cutting-speed reference by material and tool type, and a full variable reference with unit conversion notes.
Reference Tables & Conversions
A quick three-field solver, a feed rate lookup grid, and typical cutting speeds by material and tool type.
Quick feed solver — enter any two, read the third
Feed Rate Lookup — f × N
Computed from fr = f · N. Values in mm/min.
| f (mm/rev) | N = 500 | N = 1000 | N = 2000 | N = 4000 | N = 8000 | N = 16000 |
|---|
Typical Cutting Speeds and Feed Rates by Material
Representative values for HSS and carbide tooling in milling. Actual values depend on tool geometry, coolant, rigidity and depth of cut.
| Workpiece material | Cutting speed vc (m/min) | Feed per tooth fz (mm) | Typical N @ Ø10 mm (RPM) | Typical fr @ z=4 |
|---|---|---|---|---|
| Aluminium (HSS) | 150 – 400 | 0.05 – 0.15 | 4,800 – 12,700 | 950 – 7,600 mm/min |
| Aluminium (carbide) | 300 – 1000 | 0.05 – 0.20 | 9,500 – 31,800 | 1,900 – 25,400 mm/min |
| Brass and bronze | 90 – 200 | 0.04 – 0.12 | 2,900 – 6,400 | 460 – 3,070 mm/min |
| Mild steel (HSS) | 20 – 40 | 0.02 – 0.07 | 640 – 1,270 | 50 – 360 mm/min |
| Mild steel (carbide) | 80 – 200 | 0.02 – 0.10 | 2,500 – 6,400 | 200 – 2,550 mm/min |
| Alloy steel (HSS) | 15 – 30 | 0.02 – 0.06 | 480 – 950 | 40 – 230 mm/min |
| Alloy steel (carbide) | 60 – 150 | 0.02 – 0.08 | 1,900 – 4,800 | 150 – 1,540 mm/min |
| Stainless steel (HSS) | 10 – 25 | 0.015 – 0.05 | 320 – 800 | 20 – 160 mm/min |
| Stainless steel (carbide) | 40 – 100 | 0.015 – 0.06 | 1,270 – 3,180 | 80 – 760 mm/min |
| Cast iron (carbide) | 60 – 150 | 0.03 – 0.10 | 1,900 – 4,800 | 230 – 1,920 mm/min |
| Titanium alloy (carbide) | 30 – 70 | 0.01 – 0.04 | 950 – 2,230 | 40 – 360 mm/min |
| Nickel superalloy (carbide) | 15 – 40 | 0.005 – 0.03 | 480 – 1,270 | 10 – 150 mm/min |
| Hardened steel 45–55 HRC (carbide) | 20 – 60 | 0.01 – 0.04 | 640 – 1,900 | 25 – 300 mm/min |
| Plastics (HSS/carbide) | 200 – 800 | 0.05 – 0.25 | 6,400 – 25,500 | 1,280 – 25,500 mm/min |
| Composites (carbide/PCD) | 100 – 400 | 0.02 – 0.10 | 3,180 – 12,700 | 250 – 5,100 mm/min |
Variable Reference
| Symbol | Meaning | Typical range | Units |
|---|---|---|---|
| fr | Table feed rate | 0.1 – 20,000 | mm/min |
| f | Feed per revolution | 0.001 – 50 | mm/rev |
| N | Spindle speed | 1 – 10⁵ | RPM |
| fz | Feed per tooth (chip load) | 0.001 – 1 | mm/tooth |
| z | Number of teeth (flutes) | 1 – 20 | teeth |
| vc | Cutting speed | 10 – 1,000 | m/min |
| D | Tool diameter | 0.1 – 200 | mm |
| ap | Depth of cut (axial) | 0.01 – 50 | mm |
| ae | Width of cut (radial) | 0.01 – 200 | mm |
| MRR | Material removal rate | — | cm³/min |
What Does fr = f · N Measure?
The feed rate is the speed at which the cutting tool and the workpiece move relative to each other in the direction of cut. In milling, it is the table feed — the speed at which the workpiece is driven past the rotating cutter. In turning, it is the carriage feed — the rate at which the tool advances along the axis of the rotating workpiece. In drilling, it is the rate at which the drill is pushed into the material. In every case, the feed rate is chosen jointly with the spindle speed and the tool geometry to control the chip load per tooth, which is the variable that ultimately governs cutting forces, tool life and surface finish.
The formula fr = f · N is the simplest expression of the relationship between feed and speed. It says that the table feed per minute equals the feed per revolution multiplied by the number of revolutions per minute. This is directly analogous to the linear speed of a wheel: if a wheel of radius r rotates at N revolutions per minute, the point on its rim moves at 2πNr per minute. In machining the "wheel" is the cutter, and the chip load f is the distance the workpiece advances per revolution, so the table must move at f · N.
Feed Rate Formula
The defining relationship is:
Rearranged to solve for the other two unknowns:
N = fr / f
For milling, the feed per revolution is the product of feed per tooth and number of teeth:
fr = fz · z · N
fz = fr / ( z · N )
Cutting speed and material removal rate follow from the same inputs:
MRR = fr · ap · ae / 1000 (cm³/min, fr in mm/min)
Feed Variables
| Symbol | Meaning | Notes |
|---|---|---|
| fr | Table feed rate | The linear speed of the workpiece relative to the tool |
| f | Feed per revolution | Distance advanced per spindle revolution; mm/rev |
| N | Spindle speed | Rotational speed of the cutting tool or workpiece; RPM |
| fz | Feed per tooth | The chip load — the thickness of material each cutting edge removes |
| z | Number of teeth | Flutes on a milling cutter; cutting edges on a drill or reamer |
| vc | Cutting speed | The linear speed of the tool edge relative to the workpiece |
| MRR | Material removal rate | Volume of material removed per unit time; cm³/min |
How Each Variable Affects the Result
The relation is linear in both f and N — doubling either doubles the feed rate, since the table must move further per revolution or complete more revolutions per minute. This linearity is the reason that feed and speed are often grouped as "feeds and speeds" in shop-floor practice: they can be adjusted in tandem without changing the cutting geometry. If you want to run 20 % faster, increase N by 20 % and fr by 20 % together, and the chip load per tooth stays constant.
In practice, N is limited by the tool material, the workpiece material, and the spindle's maximum speed. Carbide tooling can run 3–5× faster than HSS in the same material, which is why carbide has almost entirely displaced HSS in production environments. The feed rate is limited by the machine axis capability, the rigidity of the setup, and the chip load the tool can tolerate. Chips that are too thin cause the tool to rub and work-harden the surface; chips that are too thick overload the tooth and can break it. The sweet spot for most materials is a chip load in the range of 0.02–0.20 mm/tooth for milling.
The interaction between feed and speed also affects surface finish and tool life in non-obvious ways. Higher speed with the same feed means the same chip load but a higher cutting temperature at the tool edge; this can accelerate diffusion wear on carbide tools even though the mechanical forces are unchanged. Lower speed with the same feed means the same forces but longer contact time and more opportunity for built-up edge to form; this is why very low cutting speeds are often problematic in ductile materials. The feeds-and-speeds selection is therefore a compromise between productivity, tool life and surface quality, and it is rarely as simple as reading a table.
Feed Rate Calculation Examples
fr = 0.2 × 1,500 = 300 mm/min
f = 400 / 2,000 = 0.200 mm/rev
N = 250 / 0.1 = 2,500 RPM
f = fz · z = 0.05 × 4 = 0.2 mm/rev
fr = 0.2 × 3,000 = 600 mm/min
fz = 900 / (6 × 3,000) = 0.05 mm/tooth
Frequently Asked Questions
Feed rate fr is the table speed in mm/min — the speed at which the workpiece moves past the cutter. Feed per tooth fz is the thickness of material each cutting edge removes per revolution, in mm/tooth — the chip load. They are related by the number of teeth and the spindle speed: fz = fr / (z · N). Feed rate is a machine setting that you dial in; feed per tooth is a physical property of the cut that determines whether the tool will survive. In practice, machinists choose fz from a chart (based on tool material, workpiece material and tool geometry), then compute fr = fz · z · N to program the machine.
Feed per tooth depends primarily on the tool material, the workpiece material, and the tool diameter. As a rough starting point for milling with carbide tooling: aluminium 0.05–0.20 mm/tooth, mild steel 0.03–0.10 mm/tooth, stainless steel 0.02–0.07 mm/tooth, titanium 0.01–0.04 mm/tooth, hardened steel 0.01–0.04 mm/tooth. Larger tools and stiffer setups can handle the upper end of these ranges; smaller tools and long overhangs must run at the lower end. Tool manufacturers publish recommended chip loads for each specific cutter, and these are the most reliable source. If in doubt, start conservative and increase the chip load gradually while watching for chatter, vibration and tool wear.
Because when the chip load is below a critical value, the cutting edge no longer shears the material cleanly — it rubs against the surface instead. This rubbing generates heat, promotes work-hardening of the workpiece surface, accelerates abrasive and adhesive wear on the tool edge, and produces a poor surface finish. In stainless steel and titanium alloys, work-hardening can make the next pass even harder than the first, leading to rapid tool failure. The classic advice is "never take a cut thinner than the tool's edge radius" — for a typical carbide insert, that is about 0.01–0.02 mm per tooth. If your chip load is below this, either increase the feed rate or use a tool with a sharper edge geometry.
Cutting speed vc is the linear speed of the tool edge relative to the workpiece, expressed in m/min. It is computed from the spindle speed and tool diameter: vc = π · D · N / 1000. Feed rate is the linear speed in the direction of cut, expressed in mm/min. They are orthogonal — one describes the tangential motion of the cutting edge, the other the perpendicular motion of the workpiece. Both are determined by the same combination of tool material, workpiece material and tool geometry, and both are typically read from the same feeds-and-speeds chart. The two together define the chip geometry: vc sets the deformation rate, fz sets the chip thickness, and the ratio between them defines the shear angle.
One mm/min equals 0.001 m/min, 0.01667 mm/s, 0.03937 in/min, or 0.00003937 in/s. To convert from mm/min to in/min, multiply by 0.03937. To convert from in/min to mm/min, multiply by 25.4. In CNC programming, most metric controllers use mm/min directly, while imperial controllers use in/min (often abbreviated IPM). When mixing tools and machines from different regions, always confirm which unit the controller expects — a 300 mm/min program run as 300 in/min would run 25× too fast and destroy the tool instantly.
Yes, with the same meaning but different conventions. In turning, N is the spindle speed of the rotating workpiece, and f is the feed per revolution of the tool along the axis — typically 0.05–0.5 mm/rev. In drilling, N is the spindle speed of the drill, and f is the feed per revolution of the drill into the material — typically 0.1–0.5 mm/rev for HSS drills, higher for carbide. In all three processes the table or tool must advance at f · N mm/min, so the basic relation is universal. The differences are in how fz (feed per tooth) is defined: for turning, the tool has one cutting edge so f = fz; for drilling, the drill has two cutting edges so f = 2·fz. Always check the convention your tooling data uses.
Every CNC machine specifies a maximum feed rate — typically 5,000–20,000 mm/min for a modern vertical machining centre, 10,000–40,000 mm/min for a high-speed machine, and 1,000–3,000 mm/min for an older manual machine. The limit is set by the servo motor power, the axis drive ratios, and the required acceleration. If you program a feed rate above the machine's limit, most controllers will either alarm out or clamp to the maximum value. In high-speed contouring, the effective feed rate on curved paths is further limited by the axis acceleration — the controller must slow down through tight corners to stay on the commanded path, so the actual feed rate may be well below the programmed value on intricate geometry.
As a cutting tool wears, its edge radius increases and its cutting efficiency drops. To maintain the same material removal rate and surface finish, the machinist often has to reduce the feed rate or spindle speed, or accept a lower quality of cut. In production environments, tool wear is managed by changing inserts on a schedule, or by adaptive control systems that monitor spindle load and adjust feeds and speeds in real time to maintain constant cutting conditions. The feed rate formula itself does not account for wear — it gives the kinematic relationship — but the practical choice of f and N must include an allowance for tool life, which is why shops keep detailed records of tool life for each material and operation and adjust the starting feeds and speeds accordingly.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| f_r | Feed rate | mm/min |
| f | Feed per revolution | mm/rev |
| N | Spindle rotational speed | RPM |
What it means
Feed rate (f_r) is the speed at which the cutting tool moves relative to the workpiece along the direction of feed. In turning and milling, it is often expressed in mm/min. For rotating workpieces, feed rate is calculated as f_r = f · N, where f is the feed per revolution (mm/rev) and N is the spindle speed (rpm). This parameter determines the rate of material removal and influences surface roughness, chip formation, and tool life. Higher feed rates improve productivity but may compromise surface finish and increase cutting forces. The feed per tooth in milling is similar. In CNC programming, feed rate is one of the main cutting parameters to be set. It must be optimised along with cutting speed and depth of cut. Feed rate also affects the power required and the quality of the machined surface. Understanding feed rate is essential for process planning and tool path generation. Proper selection balances productivity and quality.
Worked example
Feed Rate – Two Examples
Real‑World| Parameter | Value |
|---|---|
| f | 0.2 mm/rev |
| N | 500 RPM |
| Parameter | Value |
|---|---|
| f_z | 0.1 mm/tooth |
| z | 4 |
| N | 800 RPM |
Common mistakes
- Feed per revolution f: In mm/rev.
- Spindle speed N: In rpm.
- Units: f (mm/rev) × N (rev/min) = mm/min – correct.
- Feed rate vs. cutting speed: These are different – feed rate is the tool’s linear advance, cutting speed is surface speed.
- For milling: Feed rate may be per tooth; adjust accordingly.
Applications
Feed rate in machining is the linear speed at which the tool advances into the workpiece, calculated as feed per revolution times spindle speed. It directly affects surface roughness, tool life, and machining time. Proper feed rate selection is essential for achieving desired surface finish and dimensional accuracy while minimising tool wear. In CNC programming, feed rates are optimised based on material, tool geometry, and cutting conditions. The formula is used in process planning to calculate cycle times and to balance productivity with tool life. By carefully controlling feed rate, manufacturers can achieve high‑quality parts efficiently.
- CNC machining process planning and programming
- Surface finish and dimensional accuracy control
- Tool wear and tool life optimisation
- Cycle time estimation and productivity improvement
- Selection of machining parameters for different materials
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