Skip to main content
0 results ↑ ↓ navigate, ↵ select

Degrees to Second of arcs Converter (° to SOA)

Rate this converter 0 of 0 ratings
Instant calculation with 0ms overhead
Popular Converters
Live Conversion • ISO 80000-3:2019 Certified
1 Degree = 3600 Second of arc
1 ° = 3,600 SOA • 1 SOA = 0.000277778 °
Degree to Second of arc: One Degree is equal to 3600 Second of arcs.
Certified Authority Value
3600.00000000
SOA
Exact: 1 SOA ≡ 0.0002777777778 °
°
°
Swap to Second of arc to Degree
Swap to Second of arc to Degree
SOA
SOA 3600
Quick Values:
Conversion Formula
To convert Degree to Second of arc, multiply by 3600
° × 3600 = SOA

Calculation: 1 ° × 3600 = 3600 SOA

Common Degree to Second of arc Calculations

Quick-lookup reference table showing calculated equivalents for standard increments between Degree (°) and Second of arc (SOA).

Tap any row to calculate
Degree to Second of arc: Primary Direct Table (15 Steps)
Degree to Second of arc Conversion Reference Table
Conversion & Equivalent Value Scientific Notation
0.001 ° 3.6 SOA 3.6 × 10⁰
0.01 ° 36 SOA 3.6 × 10¹
0.1 ° 360 SOA 3.6 × 10²
0.5 ° 1800 SOA 1.8 × 10³
1 ° 3600 SOA 3.6 × 10³
2 ° 7200 SOA 7.2 × 10³
5 ° 18000 SOA 1.8 × 10⁴
10 ° 36000 SOA 3.6 × 10⁴
20 ° 72000 SOA 7.2 × 10⁴
25 ° 90000 SOA 9 × 10⁴
50 ° 180000 SOA 1.8 × 10⁵
100 ° 360000 SOA 3.6 × 10⁵
250 ° 900000 SOA 9 × 10⁵
500 ° 1800000 SOA 1.8 × 10⁶
1000 ° 3600000 SOA 3.6 × 10⁶
Second of arc to Degree: Reciprocal Summary
Second of arc to Degree Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 SOA 0.000277778 ° 2.778 × 10⁻⁴
5 SOA 0.00138889 ° 1.389 × 10⁻³
10 SOA 0.00277778 ° 2.778 × 10⁻³
50 SOA 0.0138889 ° 1.389 × 10⁻²
100 SOA 0.0277778 ° 2.778 × 10⁻²
View Complete 15-Row Second of arc to Degree Table

Real-World Context & Everyday Benchmarks

Tap to load into converter

To help contextualize these units in everyday life, science, and engineering, here are verified real-world reference points for Degree (°) and Second of arc (SOA):

Degree References:

  • Perpendicular orthogonal intersection right angle (90°) 90 °
  • Straight line flat angle rotation in Euclidean plane geometry (180°) 180 °
  • Complete 360-degree full circle revolution rotation (360°) 360 °
  • Equilateral triangle internal corner interior angle (60°) 60 °

Second of arc References:

  • Subtended angle of arc equal in length to circle radius (~57.3°) 206264.81 SOA
  • Complete circular rotation angle expressed in radians (2π rad / 6.283 rad) 1295961.78 SOA

Tap any benchmark above to automatically calculate its exact equivalent in Second of arc.

ISQ Dimension: Dimensionless [L / L] Coherent SI Unit: radian (rad) Geoscience, Geodesy & Petroleum Engineering

How to Convert Degree to Second of arc

Converting Degree (°) to Second of arc (SOA) is a core calculation in Plane Angle, which measures the circular arc subtended between two intersecting rays or diverging lines. Because Degree represents a larger magnitude than Second of arc, converting from ° to SOA expands the numerical figure. Exactly 1 Degree encompasses 3600 Second of arc. To convert any quantity, multiply the value in Degree by 3600.

Direct Factor1 ° = 3600 SOA
Inverse Ratio1 SOA = 0.000277778 °
Conversion ScaleDirect Proportional Magnitude Expansion
First-Principles SI Derivation ProofNIST SP 811 / ISO 80000 Compliance

Mathematical Conversion Derivation via Coherent SI Base Unit

Under the International System of Quantities (ISQ), dimensional conversion between non-SI units is rigorously resolved by bridging through the coherent SI base unit (radian (rad)) without arbitrary rounding:

Vtarget=Vsource×(ksource→SIktarget→SI)V_{\text{target}} = V_{\text{source}} \times \left( \frac{k_{\text{source} \to \text{SI}}}{k_{\text{target} \to \text{SI}}} \right)
Universal Dimensional Conversion Law (ISO 80000 / NIST SP 811)
1. Source SI Bridge (ksource):1 ° = 1 radian (rad)
2. Target SI Bridge (ktarget):1 SOA = 0.000277778 radian (rad)
Step-by-step substitution for Degree → Second of arc:V(SOA) = V(°) × ( 1 / 0.000277778 ) = V(°) × 3600
Mathematical FormulaValue in Second of arc = Value in Degree × 3600Direct computational formula applied for standard conversion.
Worked Example

For an engineering input of 36 °, applying the conversion factor yields exactly 129600 SOA. At larger operational scale, 240 Degree corresponds to 864000 SOA.

Inverse check: 1 SOA = 0.000277778 °.

Understanding Degree and Second of arc

Degree

°
SI Base Standard

A Degree (°) is the official base standard unit for plane angle.

Applications & Practical Context

In practical angle terms, a perpendicular orthogonal intersection right angle (90°) equals 90 °, a straight line flat angle rotation in Euclidean plane geometry (180°) equals 180 °, a complete 360-degree full circle revolution rotation (360°) equals 360 °.

Physical Setup

A plane angle of 1 ° represents the angular divergence subtending an arc equal to 1 Degree.

Conversion to SI Unit: radian (rad)
1 ° = 1 rad (Base Standard)

Second of arc

SOA
Standard Unit

A Second of arc (SOA) is a recognized unit for plane angle.

Applications & Practical Context

In practical angle terms, a subtended angle of arc equal in length to circle radius (~57.3°) equals 206264.81 SOA, a complete circular rotation angle expressed in radians (2π rad / 6.283 rad) equals 1295961.78 SOA.

Physical Setup

A physical magnitude of 1 SOA corresponds to 0.000277778 rad in standard SI measurement.

Conversion to SI Unit: radian (rad)
1 SOA = 0.000277778 rad

Domain Metrology & Engineering Applications

Governing Law & Equation

Subtended Circular Arc Ratio (θ = s / r)

Measurement Instrumentation

Rigorously quantified in laboratory and field settings using electronic digital theodolites, optical polygon autocollimators, and rotary optical angle encoders.

Primary Industry Sectors

Applied across geodetic triangulation surveys, aerospace satellite gimbal tracking, civil bridge alignment, and telescope mount tracking under international metrology standard ISO 80000-3:2019.

Physical Orders of Magnitude & Laboratory Reference Benchmarks

Physical Phenomenon / Engineering ReferenceReference ValueConverted to Second of arc
Perpendicular orthogonal intersection right angle (90°)90 °324000 SOA
Straight line flat angle rotation in Euclidean plane geometry (180°)180 °648000 SOA
Complete 360-degree full circle revolution rotation (360°)360 °1296000 SOA
Equilateral triangle internal corner interior angle (60°)60 °216000 SOA
Institutional Metrology & Standard Authority:

Formulas, conversion coefficients, and base definitions on this page strictly adhere to the ISO 80000-3:2019 and the BIPM SI Brochure (9th Edition). Governed by Subtended Circular Arc Ratio (θ = s / r) under ISO 80000 dimensional vector Dimensionless [L / L].

Multi-Variable Engineering Bridge Trigonometry & Circular Trajectory

Angular Rotation to Tangential Arc Length Bridge (Meters • Centimeters • Millimeters • Kilometers • Feet • Inches)

Calculate curved perimeter arc length s = r × θ × (π/180) subtended along circular trajectories, bridging angular rotation and travel distance [L] via radius (r).

s = r × θ × (π/180)
Vector: [°] × [π/180 rad/°] × [m] → [m]
Live Calculated Bridge Equivalent:
1 ° at 28" Commuter Bicycle Wheel (0.35 m) = 0.006109 m
Equals 6.1087 × 10⁻⁶ km • 0.6109 cm • 6.1087 mm
SI Length
0.006109
m
Meters
Geographic Scale
6.1087 × 10⁻⁶
km
Kilometers
Engineering Scale
0.6109
cm
Centimeters
Precision Machining
6.1087
mm
Millimeters
US Architectural
0.02004
ft
Feet
US Tooling
0.2405
in
Inches
  1. 1. Normalize Input to SI Base Unit (°):
    θ = 1 ° × 1 = 1 °
  2. 2. Apply Engineering Parameter (r):
    Selected condition: 28" Commuter Bicycle Wheel (0.35 m) at r = 0.35 m
  3. 3. Execute Governing Physical Law in SI Units:
    s = r × θ × (π/180) = (0.01745 rad/°) × (0.35 m) × (1 °) = 0.00610865 m
  4. 4. Convert to Standard Engineering Units:
    • m: 0.00610865 × 1 = 0.006109 m (Meters) • km: 0.00610865 × 0.001 = 6.1087 × 10⁻⁶ km (Kilometers) • cm: 0.00610865 × 100 = 0.6109 cm (Centimeters) • mm: 0.00610865 × 1000 = 6.1087 mm (Millimeters) • ft: 0.00610865 × 3.2808 = 0.02004 ft (Feet) • in: 0.00610865 × 39.3701 = 0.2405 in (Inches)
Explore Arc Length Converter →
Engineering Substance / Operating Standard Parameter Value (m) Reference State / Condition Typical Industrial & Engineering Application
Wall Clock Minute Hand (0.15 m) 0.15 0.15 m (150 mm) Mechanical analog clock tip trajectory radius (15 cm)
28" Commuter Bicycle Wheel (0.35 m) 0.35 0.35 m (350 mm) Standard 700c tire tread rolling radius
Utility Wind Turbine Blade (60 m) 60 60.0 meters Offshore 4 MW turbine blade tip rotation perimeter
Earth Equatorial Radius (6,378 km) 6378137 6,378,137 meters WGS 84 terrestrial equatorial geographic radius
Geostationary Orbital Radius (42,164 km) 4.2164 × 10⁷ 42,164,000 meters Satellite geosynchronous orbital perimeter radius
Embed
Need this Degree to Second of arc calculator on your website, lab portal, or research blog?
Free HTML Widget 100% Responsive Zero Cookie Tracking
Notice a calculation discrepancy, rounding error, or glitch?
Help us maintain 100% scientific precision and report any issues directly to engineering.

Frequently Asked Questions

There are exactly 3600 second of arcs (SOA) in 1 degree (°). To calculate larger amounts manually, simply multiply your total number of degrees by the conversion multiplier of 3600.

The mathematical formula to convert degrees to second of arcs is: [value] * 3600 = second of arcs. Rather than doing the math manually, you can use our high-precision online calculator to process this exact equation instantly without rounding errors.

To perform the reverse calculation from second of arcs back to degrees, you must divide your starting value by 3600. Our bidirectional tool automatically computes this inverse equation the moment you type into the second of arc input field.

1 Degree is larger than 1 Second of arc. Specifically, 1 Degree equals exactly 3600 second of arcs, making it 3600 times larger (a difference of 3.56 orders of magnitude). Therefore, quantities expressed in second of arcs require a larger numerical value to represent the same physical amount.

A typical perpendicular orthogonal intersection right angle (90°) measures 90 °, which corresponds to 324000 Second Of Arc (Second of arc).

Physically Coupled Geoscience & Geodesy Converters

Explore interconnected physical dimension converters within the Geoscience & Geodesy cluster (ISO 80000-3:2019 / IUGG Geodetic Reference System).

View Hub
Geological Permeability Dimensional Hub & Tools
Time Dimensional Hub & Tools