The Cinematography Shutter Angle to Shutter Speed Exposure Sizer provides an interactive three-parameter algebraic modeling interface for exploring cinema rotary shutter angles, camera frame rates, and motion blur exposure ratios.

### Algebraic Ratio Formulation The component evaluates camera exposure variables using three generalized algebraic relationships: - Primary Metric: $(val_1 \times val_2) / \max(0.01, val_3)$. In optical motion camera modeling, this represents scaled photographic exposure duration relative to ND filter attenuation. - Geometric Mean (Secondary Index): $\sqrt{\max(0, val_1 \times val_2)}$, modeling geometric center exposure indices. - Efficiency Ratio (%): $\min(100, \max(0, (val_1 / (val_1 + val_2)) \times 100))$, modeling proportional rotary shutter opening angle.

### Note on Optical Cinema Physics & The 180-Degree Rule This calculator computes a generalized three-parameter algebraic proxy. In motion picture cinematography, physical rotary disc shutters control exposure time ($T_{\text{exposure}}$) through an angular opening ($\theta$) relative to film frame rate ($FPS$): - Exact Shutter Speed Formula: $$T_{\text{exposure}} = \frac{\theta}{360^\circ \times FPS}\text{ seconds}$$ - Standard 180° Cinematic Shutter: At the standard cinema rate of $24\text{ FPS}$, an angular opening of $180^\circ$ produces: $$T_{\text{exposure}} = \frac{180}{360 \times 24} = \frac{1}{48}\text{ second}$$ - Creative Shutter Variations: Narrower angles ($45^\circ$ or $90^\circ$) yield crisp, staccato action sequences with minimal motion blur, while wider angles ($270^\circ$ or $360^\circ$) produce exaggerated motion smearing and maximum low-light light gathering.

### Worked Numeric Example Using default component parameter values: - Primary Dimension / Load ($val_1$): 100 - Operating Coefficient ($val_2$): 20 - Safety Factor / Loss Ratio ($val_3$): 5 - Evaluated Outputs: - Primary Metric: $(100 \times 20) / 5 = 400.00$ - Geometric Mean: $\sqrt{100 \times 20} = \sqrt{2000} \approx 44.72$ - Efficiency Ratio: $(100 / (100 + 20)) \times 100 = 83.33\%$

### In-Browser Calculation Note All cinematography exposure equations evaluate purely inside your browser JavaScript runtime with zero telemetry or network calls.