Engineering Reference: Unit Conversion Tables
Basic Formulae
Motor Constants
Servo Motor Formulae
Conversions:
Length
Mass
Force
Torque
Power
Linear Velocity
Angular Velocity
Rotary Inertia
Common Engineering Unit Conversions - Basic Units
| Parameter (Basic Units) |
SI Units |
English/American Units |
| mass (m) |
kilogram (kg) |
pound mass (lbm) |
| length - distance (L) |
meter (m) |
foot or inch (ft or in) |
| time (t) |
second (s) |
| current (I) |
Ampere (A) |
Derived Units
| Parameter (Derived Units) |
SI Units |
English/American Units |
| Force - weight (F or W) |
Newton (N) |
pound or ounce (lbf or oz) |
| Torque (T) |
Newton-meter (Nm) |
foot-pound (ft-lb or in-lb) |
| Work - energy (W or E) |
Joule (J) |
foot-pound (ft-lb or in-lb |
| Power (P) |
Watt (W) |
horsepower (hp or W) |
| Voltage, EMF (V) |
Volt (V) |
| Resistance (R) |
ohms (Ω) |
| Inertia (J) |
kilogram-meter2 (kg-m2) |
inch-pound-second2 (in-lb-s2) |
| plane angle (α, β, γ, etc.) |
radian (rad) |
degree or radian (deg or rad) |
| rotation (Ө) |
revolution (rev) |
| velocity - linear (v) |
meter per sec. (m/s) |
inch per second (in/s) |
| acceleration (a) |
meter per second2 (m/s2) |
inch per second2 (in/s2) |
| velocity - angular (ω) |
rad per second (rad/s) |
| velocity - rotational (ω) |
rev per minute (rpm) |
| accel - angular (α) |
rad per second2 (rad/s2) |
Basic Definitions & Formulae
| Parameter Formula |
SI Units Formula |
English/American Units Formula |
| Force - accel (F = m * a) |
1 N = 1 kg * 1 m / s2 |
1 lbf = 1 lbf / (386 in / s2) * 386 in / s2 |
| Torque - accel (T = J * α) |
1 Nm = 1 kg-m2 * 1 rad / s2 |
1 in-lb = 1 in-bl-s2 * 1 rad / s2 |
| Voltage, EMF (V = I * R) |
1 V = 1 A * 1 Ω |
| Work - Energy (E = F * L) |
1 J = 1 N * 1 m |
1 in-lb = .113 Nm = .113 Ws = .113 J |
| Energy - elect (E = V * I * t) |
1 J = 1 V * 1 A * 1 s |
| Power (P = F * v) |
1 W = 1 N * 1 m / s |
1 hp = 550 ft-lb / s = 745.7 W |
| Power (P = T * ω) |
1 W = 1 Nm * 1 rad / s |
(note: radians have no units) |
| Power (P = V * I) |
1 W = 1 V * 1 A |
| Power (P = E / t) |
1 W = 1 J / 1 s |
| Power (P = I2 * R) |
1 W = 1 A2 * 1 Ω |
Motor Constants
| Parameter Formula |
SI Units Formula |
English/American Units Formula |
| Torque const (Kt = T / I) |
Kt = Nm / A |
Kt = in-lb / A |
| Voltage const (Ke = V / ω) |
Ke = V / (rad / s) |
Ke = V / krpm |
Servo Motor Formulae
| Parameter Formula |
SI Units Formula |
English/American Units Formula |
| Current Draw (I + T / Kt) |
1 A = 1 Nm / (Nm / A) |
1 A = 1 in-lb / (in-lb / A) |
| Voltage Required (V = IRa + Ke * ω) |
1 V = AΩ + V / (rad / s) * (rad / s) |
1 V = AΩ + V / (krpm) * (krpm) |
Conversions:
To convert from units of A to units of B, find the value at the intersection of A and B, then multiply your number by this value. Example: to convert from cm to microns, multiply value in cm by 1.00E+04.
Length Conversion
| A (below) B (right) |
micron (µm) |
mm |
cm |
m |
in |
ft |
| micron (µm) |
1 |
0.001 |
1.00E-04 |
1.00E-06 |
3.94E-05 |
3.28E-06 |
| mm |
1000 |
1 |
0.1 |
0.001 |
0.03937 |
3.28E-03 |
| cm |
1.00E+04 |
10 |
1 |
0.01 |
0.3937 |
0.03281 |
| m |
1.00E+06 |
1000 |
100 |
1 |
39.37 |
3.281 |
| in |
2.54E+04 |
25.4 |
2.54 |
0.0254 |
1 |
0.0833 |
| ft |
3.05E+05 |
304.8 |
30.48 |
0.3048 |
12 |
1 |
Mass Conversion
| A (below) B (right) |
g |
kg |
slug |
ozm |
lbm |
| g |
1 |
0.001 |
6.85E-05 |
0.0353 |
2.20E-03 |
| kg |
1000 |
1 |
6.85E-02 |
35.274 |
2.2046 |
| slug |
1.46E+04 |
14.59 |
1 |
514.78 |
32.17 |
| ozm |
28.35 |
0.0284 |
1.94E-03 |
1 |
0.0625 |
| lbm |
453.6 |
0.4536 |
0.0311 |
16 |
1 |
Force Conversion
| A (below) B (right) |
N |
kgf |
gf |
ozf |
lbf |
| N |
1 |
0.102 |
101.97 |
3.596 |
0.225 |
| kgf |
9.81 |
1 |
1000 |
35.274 |
2.205 |
| gf |
9.81E-03 |
0.001 |
1 |
0.0353 |
2.21E-03 |
| ozf |
0.28 |
0.0283 |
28.35 |
1 |
0.0625 |
| lbf |
4.45 |
0.4536 |
453.6 |
16 |
1 |
Torque Conversion
| A (below) B (right) |
g-cm |
kg-cm |
kg-m |
N-m |
oz-in |
lb-in |
lb-ft |
| g-cm |
1 |
0.001 |
1.00E-05 |
9.81E-05 |
0.014 |
8.68E-04 |
7.23E-05 |
| kg-cm |
1000 |
1 |
0.01 |
0.098 |
13.89 |
0.868 |
0.072 |
| kg-m |
1.00E+05 |
100 |
1 |
9.81 |
1389 |
86.8 |
7.23 |
| N-m |
1.02E+04 |
10.2 |
0.102 |
1 |
141.6 |
8.85 |
0.738 |
| oz-in |
72.01 |
0.072 |
7.21E-04 |
7.06E-03 |
1 |
0.063 |
5.21E-03 |
| lb-in |
1.15E+03 |
1.152 |
0.012 |
0.113 |
16 |
1 |
0.083 |
| lb-ft |
1.38E+04 |
13.83 |
0.138 |
1.356 |
192 |
12 |
1 |
Power Conversion
| A (below) B (right) |
Watts |
kW |
Horsepower |
in-lb/s |
ft-lb/s |
| Watts |
1 |
100E-03 |
1.34E-03 |
8.85 |
0.74 |
| kW |
1000 |
1 |
1.34 |
8851 |
738 |
| Horsepower |
746 |
0.746 |
1 |
6600 |
550 |
| in-lb/s |
0.113 |
1.13E-04 |
1.52E-04 |
1 |
0.083 |
| ft-lb/s |
1.35 |
1.36E-03 |
1.82E-03 |
12 |
1 |
Linear Velocity Conversion
| A (below) B (right) |
mm/s |
cm/s |
m/s |
in/s |
ft/s |
in/min |
ft/min |
| mm/s |
1 |
0.1 |
0.001 |
0.0394 |
3.28E-03 |
2.362 |
0.1968 |
| cm/s |
10 |
1 |
0.01 |
0.394 |
0.0328 |
23.62 |
1.97 |
| m/s |
1000 |
100 |
1 |
39.37 |
3.281 |
2362.2 |
196.9 |
| in/s |
25.4 |
2.54 |
0.0254 |
1 |
0.083 |
60 |
5 |
| ft/s |
304.8 |
30.48 |
0.3048 |
12 |
1 |
720 |
60 |
| in/min |
0.423 |
0.0423 |
4.23E-04 |
0.0167 |
1.39E-03 |
1 |
0.0833 |
| ft/min |
5.08 |
0.508 |
5.08E-03 |
0.2 |
0.0167 |
12 |
1 |
Angular Velocity Conversion
| A (below) B (right) |
deg/s |
rad/s |
rpm |
rps |
| deg/s |
1 |
0.0175 |
0.167 |
2.78E-03 |
| rad/s |
57.3 |
1 |
9.55 |
0.159 |
| rpm |
6 |
0.105 |
1 |
0.0167 |
| rps |
360 |
6.28 |
60 |
1 |
Rotary Inertia Conversion
| A (below) B (right) |
g-cm2 |
kg-cm2 |
g-cm-s2 |
kg-cm-s2 |
kg-m2 |
lb-in-s2 |
lb-ft-s2 |
lb-in2 |
lb-ft2 |
oz-in2 |
oz-in-s2 |
| g-cm2 |
1 |
0.001 |
0.001 |
1.02E-06 |
1.00E-07 |
8.85E-07 |
7.38E-08 |
3.42E-04 |
2.37E-06 |
5.50E-03 |
1.42E-05 |
| kg-cm2 |
1000 |
1 |
1.02 |
0.001 |
0.0001 |
8.85E-04 |
7.38E-05 |
0.342 |
2.40E-03 |
5.47 |
0.014 |
| g-cm-s2 |
981 |
0.981 |
1 |
0.001 |
9.81E-05 |
8.68E-04 |
7.23E-05 |
0.335 |
2.30E-03 |
5.36 |
0.014 |
| kg-cm-s2 |
9.81E+05 |
981 |
1000 |
1 |
0.0981 |
0.868 |
0.072 |
335.1 |
2.33 |
5362 |
13.89 |
| kg-m2 |
1.00E+07 |
10000 |
10190 |
10.19 |
1 |
8.85 |
0.738 |
3417.74 |
23.734 |
54675 |
141.6 |
| lb-in-s2 |
1.13E+06 |
1130 |
1.15E+03 |
1.152 |
0.113 |
1 |
0.083 |
386.1 |
2.68 |
6177 |
16 |
| lb-ft-s2 |
1.36E+07 |
1.36E+04 |
1.38E+04 |
13.83 |
1.36 |
12 |
1 |
4633 |
32.2 |
7.41E+04 |
192 |
| lb-in2 |
2926 |
2.93 |
2.98 |
0.003 |
2.93E-04 |
2.60E-03 |
2.16E-04 |
1 |
6.90E-03 |
16 |
0.041 |
| lb-ft2 |
4.21E+05 |
421.4 |
429.7 |
0.43 |
0.0421 |
0.373 |
0.031 |
144 |
1 |
2304 |
5.97 |
| oz-in2 |
182.9 |
0.183 |
0.187 |
1.87E-04 |
1.83E-05 |
1.62E-04 |
1.35E-05 |
0.0625 |
4.34E-04 |
1 |
2.60E-03 |
| oz-in-s2 |
7.06E+04 |
70.62 |
72 |
0.072 |
0.007 |
0.063 |
5.20E-03 |
24.13 |
0.168 |
386.1 |
1 |
