Angle Measurement Calculator
Convert between degrees-minutes-seconds (DMS), decimal degrees, and radians. Essential for precision machining and sine bar setups.
✓ DMS ↔ decimal degree conversion
✓ Degree ↔ radian conversion
✓ Sine bar height from any format
Degrees, minutes, seconds
Gage Block Height
2.5000 in
= 63.5000 mm
Quick reference — Gage block heights (inches)
| Angle | 5″ bar | 10″ bar |
|---|---|---|
| 5° | 0.4358 | 0.8716 |
| 10° | 0.8682 | 1.7365 |
| 15° | 1.2941 | 2.5882 |
| 20° | 1.7101 | 3.4202 |
| 25° | 2.1131 | 4.2262 |
| 30° | 2.5000 | 5.0000 |
| 35° | 2.8679 | 5.7358 |
| 40° | 3.2139 | 6.4279 |
| 45° | 3.5355 | 7.0711 |
Angle Conversion Formulas
Different fields use different angle formats. Machining and surveying commonly use degrees-minutes-seconds (DMS), while engineering calculations often require decimal degrees or radians.
DMS to Decimal Degrees
DD = D + (M / 60) + (S / 3600)
Example: 30°15'45” = 30 + 15/60 + 45/3600 = 30.2625°
Decimal Degrees to DMS
D = integer part of decimal degrees
M = integer part of (fractional part × 60)
S = remaining fractional minutes × 60
Example: 30.2625° = 30° 15' 45”
Degrees to Radians
Radians = Degrees × (π / 180)
90° = π/2 = 1.5708 rad
45° = π/4 = 0.7854 rad
30° = π/6 = 0.5236 rad
Why Precision Matters in Machining
In precision machining, even 1 minute of arc (1/60th of a degree) matters. On a 5” sine bar, 1 minute of error translates to approximately 0.0015” of height error. For tight-tolerance work, angles must be specified to the nearest second.
📏 Quick Reference
1° = 60 minutes = 3,600 seconds. 1 radian = 57.2958°. Full circle = 360° = 2π radians. Right angle = 90° = π/2 radians.