HomeCalculatorsPhysicsProjectile Trajectory Calculator
Physics calculator

Projectile Trajectory Calculator

R = v₀² sin(2θ) / g. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 2/2 declared partitions (trajectory, invalid-domain) · Matrix
Known limitations
  • No drag; level ground
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
R = v₀² sin(2θ) / g
Scope
Documented on page
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
1/1 property · digest 1739df87d157
Legacy regression
3/3 tests · Production surface contract 4/4
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session.
Supplemental domain review
Internal · Pass
Named expert review
Not performed
CVP suite
1/1 golden · 1/1 CVP boundary · 1/1 invalid · 1/1 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • Intro physics / NIST units — standard relations
  • Intro kinematics / projectile texts — Flat-ground trajectory
Sources
Evidence
1 legacy golden · 1 legacy boundary · legacy regression suite · 1/1 oracle-backed golden · 1/1 invalid · Artifact integrity PASS · CalculatorX electrical review
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

PrimaryR = v0² · sin(2θ) / g
iSI units unless noted.

How to use

1

Enter known values

Leave the unknown for the API mode to solve.

2

Confirm units

Use SI units unless noted.

3

Read the result

R = v₀² sin(2θ) / g

Example calculations

Common configurations with formula and result.

ϟ

Example

validation

—
v0=20 m/s, θ=45° → R≈40.8 m

Projectile Trajectory calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-09

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review

Definition
R = v₀² sin(2θ) / g
What it calculates
R = v₀² sin(2θ) / g
Inputs
  • see form
Outputs
  • see API
Formula
see formulas
Assumptions
  • Documented on page
Units
  • SI
Boundary conditions
  • coded hard errors
Example
v0=20 m/s, θ=45° → R≈40.8 m
Validation cases

1 published on this page · 3/3 tests · Production surface contract 4/4 · View evidence

  • see suite → see suite
Sources
  • Intro physics / NIST units — standard relations
    Supports: engine formulas
  • Intro kinematics / projectile texts — Flat-ground trajectory
    Supports: R = v0² sin(2θ)/g
Last reviewed
2026-08-09
Reviewed by
CalculatorX electrical review
Calculation version
1.0.0

Background

Interpretation and common distinctions.

R = v₀² sin(2θ) / g

Supported and not supported

Supported — API physics.kinematics.trajectory

Not supported — Air drag, uneven ground

Agent / API notes

Capability id: physics.kinematics.trajectory · tool id: trajectory · pin 1.0.0.

Other calculators in this family: Projectile, Centripetal .

P Projectile › F Centripetal ›
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Frequently asked questions

Key distinctions behind the calculation.

What does the API reject?

Hard validation errors such as missing inputs or out-of-range values.