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Second of arcs to Minute of arcs Converter (SOA to MOA)

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Live Conversion • ISO 80000-3:2019 Certified
1 Second of arc = 0.016666667 Minute of arc
1 SOA = 0.0166667 MOA • 1 MOA = 60 SOA
Second of arc to Minute of arc: One Second of arc is equal to 0.016666667 Minute of arcs.
Certified Authority Value
0.01666667
MOA
Exact: 1 MOA ≡ 60 SOA
SOA
SOA
Swap to Minute of arc to Second of arc
Swap to Minute of arc to Second of arc
MOA
MOA 0.016666667
Quick Values:
Conversion Formula
To convert Second of arc to Minute of arc, multiply by 0.016666667
SOA × 0.016666667 = MOA

Calculation: 1 SOA × 0.016666667 = 0.016666667 MOA

Common Second of arc to Minute of arc Calculations

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

Tap any row to calculate
Second of arc to Minute of arc: Primary Direct Table (15 Steps)
Second of arc to Minute of arc Conversion Reference Table
Conversion & Equivalent Value Scientific Notation
0.001 SOA 1.666667 × 10⁻⁵ MOA 1.667 × 10⁻⁵
0.01 SOA 0.000166667 MOA 1.667 × 10⁻⁴
0.1 SOA 0.00166667 MOA 1.667 × 10⁻³
0.5 SOA 0.00833333 MOA 8.333 × 10⁻³
1 SOA 0.0166667 MOA 1.667 × 10⁻²
2 SOA 0.0333333 MOA 3.333 × 10⁻²
5 SOA 0.0833333 MOA 8.333 × 10⁻²
10 SOA 0.166667 MOA 1.667 × 10⁻¹
20 SOA 0.333333 MOA 3.333 × 10⁻¹
25 SOA 0.416667 MOA 4.167 × 10⁻¹
50 SOA 0.833333 MOA 8.333 × 10⁻¹
100 SOA 1.666667 MOA 1.667 × 10⁰
250 SOA 4.166667 MOA 4.167 × 10⁰
500 SOA 8.333333 MOA 8.333 × 10⁰
1000 SOA 16.666667 MOA 1.667 × 10¹
Minute of arc to Second of arc: Reciprocal Summary
Minute of arc to Second of arc Conversion Reference Table
Reciprocal & Equivalent Value Scientific Notation
1 MOA 60 SOA 6 × 10¹
5 MOA 300 SOA 3 × 10²
10 MOA 600 SOA 6 × 10²
50 MOA 3000 SOA 3 × 10³
100 MOA 6000 SOA 6 × 10³
View Complete 15-Row Minute of arc to Second of arc Table

Real-World Context & Everyday Benchmarks

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

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

Minute of arc References:

  • Subtended angle of arc equal in length to circle radius (~57.3°) 3437.75 MOA
  • Complete circular rotation angle expressed in radians (2π rad / 6.283 rad) 21599.36 MOA

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

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

How to Convert Second of arc to Minute of arc

Converting Second of arc (SOA) to Minute of arc (MOA) is a core calculation in Plane Angle, which measures the circular arc subtended between two intersecting rays or diverging lines. Because Minute of arc is a broader physical scale than Second of arc, converting from SOA to MOA condenses the numerical figure. It takes 60 Second of arc to equal a single Minute of arc (1 SOA = 0.0166667 MOA). To convert any quantity, multiply by 0.0166667 (or divide by 60).

Direct Factor1 SOA = 0.0166667 MOA
Inverse Ratio1 MOA = 60 SOA
Conversion ScaleDirect Proportional Magnitude Compression
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 SOA = 0.000277778 radian (rad)
2. Target SI Bridge (ktarget):1 MOA = 0.0166667 radian (rad)
Step-by-step substitution for Second of arc → Minute of arc:V(MOA) = V(SOA) × ( 0.000277778 / 0.0166667 ) = V(SOA) × 0.0166667
Mathematical FormulaValue in Minute of arc = Value in Second of arc × 0.016666667Direct computational formula applied for standard conversion.
Worked Example

Evaluating an input of 2.5 Second of arc (SOA) produces 0.0416667 Minute of arc (MOA). In heavy-duty utility and industrial workloads, 240 SOA equals 4 MOA.

Inverse check: 1 MOA = 60 SOA.

Understanding Second of arc and Minute of arc

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

Minute of arc

MOA
Standard Unit

A Minute of arc (MOA) 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 3437.75 MOA, a complete circular rotation angle expressed in radians (2π rad / 6.283 rad) equals 21599.36 MOA.

Physical Setup

A physical magnitude of 1 MOA corresponds to 0.0166667 rad in standard SI measurement.

Conversion to SI Unit: radian (rad)
1 MOA = 0.0166667 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 Minute of arc
Perpendicular orthogonal intersection right angle (90°)90 °1.5 MOA
Straight line flat angle rotation in Euclidean plane geometry (180°)180 °3 MOA
Complete 360-degree full circle revolution rotation (360°)360 °6 MOA
Equilateral triangle internal corner interior angle (60°)60 °1 MOA
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 SOA at 28" Commuter Bicycle Wheel (0.35 m) = 1.6968 × 10⁻⁶ m
Equals 1.6968 × 10⁻⁹ km • 0.0001697 cm • 0.001697 mm
SI Length
1.6968 × 10⁻⁶
m
Meters
Geographic Scale
1.6968 × 10⁻⁹
km
Kilometers
Engineering Scale
0.0001697
cm
Centimeters
Precision Machining
0.001697
mm
Millimeters
US Architectural
5.5671 × 10⁻⁶
ft
Feet
US Tooling
6.6805 × 10⁻⁵
in
Inches
  1. 1. Normalize Input to SI Base Unit (°):
    θ = 1 SOA × 0.00027778 = 0.00027778 °
  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) × (0.00027778 °) = 1.696848 × 10⁻⁶ m
  4. 4. Convert to Standard Engineering Units:
    • m: 1.696848 × 10⁻⁶ × 1 = 1.6968 × 10⁻⁶ m (Meters) • km: 1.696848 × 10⁻⁶ × 0.001 = 1.6968 × 10⁻⁹ km (Kilometers) • cm: 1.696848 × 10⁻⁶ × 100 = 0.0001697 cm (Centimeters) • mm: 1.696848 × 10⁻⁶ × 1000 = 0.001697 mm (Millimeters) • ft: 1.696848 × 10⁻⁶ × 3.2808 = 5.5671 × 10⁻⁶ ft (Feet) • in: 1.696848 × 10⁻⁶ × 39.3701 = 6.6805 × 10⁻⁵ 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
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Frequently Asked Questions

There are exactly 0.016666667 minute of arcs (MOA) in 1 second of arc (SOA). To calculate larger amounts manually, simply multiply your total number of second of arcs by the conversion multiplier of 0.016666667.

The mathematical formula to convert second of arcs to minute of arcs is: [value] * 0.016666667 = minute 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 minute of arcs back to second of arcs, you must divide your starting value by 0.016666667. Our bidirectional tool automatically computes this inverse equation the moment you type into the minute of arc input field.

1 Minute of arc is larger than 1 Second of arc. Specifically, 1 Second of arc equals 0.016666667 minute of arcs, meaning 1 Minute of arc is 60 times larger than 1 Second of arc (a difference of 1.78 orders of magnitude). Expressing measurements in second of arcs requires a larger numerical value to represent the equivalent physical magnitude.

Under standard international measurement guidelines, 1 Second of arc converts to 0.016666667 minute of arcs. Precise numerical conversion factors ensure consistency across laboratory, engineering, and field data.

Related Second of arc and Minute of arc Conversions

Convert Second of arc to Other Units

Convert Other Units to Minute of arc

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