Tax · super (composes 4 primitives)
Backdoor + mega-backdoor Roth
Type your income, traditional IRA balance, and 401(k) plan features. We chain direct-Roth eligibility, the backdoor pro-rata trap, mega-backdoor capacity (after-tax + in-service rollover), total annual Roth, and 30-year tax-free growth value.
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Inputs
Result
Total annual Roth capacity $2,579: $0 direct + $2,579 backdoor + $0 mega-backdoor.
Clean pro-rata first: Roll your $12,000 traditional INTO your 401(k) (if plan allows) BEFORE doing the backdoor. Saves $1,415 in current-year tax.
- 1
Direct Roth eligibility (MAGI $285,000)
$0
Phased between $246,000 and $256,000
- 2
Backdoor Roth path
63% pro-rata tax
Existing $12,000 traditional balance triggers pro-rata. $1,415 tax cost on conversion. Roll traditional INTO your 401(k) to clean the path.
- 3
Pro-rata rule cost
$1,415
Reverse-rollover the Traditional into your 401(k) FIRST (if plan accepts) to clean the path before backdoor.
- 4
Mega-backdoor capacity (after-tax + rollover)
$0
Plan doesn't support — biggest leverage requires a yes-with-rollover plan.
- 5
Total annual Roth capacity
$2,579
Sum of direct + backdoor + mega-backdoor
- 6
30-year value (7% real)
$243,609
$77,368 contributed → $166,241 tax-free gains
- 7
Tax saved over 30 yrs (vs taxable)
$39,565
$166,241 of tax-free gains × 23.8% LTCG+NIIT — what you'd owe in a taxable account
Assumptions & notes
- 2026 IRA limit: $7,000 ($8,000 with 50+ catch-up). 401(k) employee deferral: $23,500 ($31,000 with catch-up).
- Total 401(k) contribution limit (employee + employer + after-tax): $70,000 ($77,500 with catch-up).
- Pro-rata rule (IRC §408(d)(2)) applies to ALL traditional IRA balances combined — including SEP-IRA and SIMPLE-IRA. Solo 401(k) is separate.
- Mega-backdoor only works at plans that allow after-tax contributions (~40% of plans) AND in-service rollover (smaller subset). Big-tech plans often have it; many smaller employers don't.
Multi-scenario comparison
What if — ±20% on one input
| Scenario | Modified AGI (MAGI) | Headline | Δ vs baseline | Magnitude |
|---|---|---|---|---|
| −20% (cautious) | $228,000 | Total annual Roth capacity $9,579: $7,000 direct + $2,579 backdoor + $0 mega-backdoor. | +$7,000 | |
| Baseline | $285,000 | Total annual Roth capacity $2,579: $0 direct + $2,579 backdoor + $0 mega-backdoor. | 0 | |
| +20% (aggressive) | $342,000 | Total annual Roth capacity $2,579: $0 direct + $2,579 backdoor + $0 mega-backdoor. | 0 |
Try the input with the highest sensitivity (above). The Δ column shows the dollar swing from a 20% move — that's how much room you have for a counter, raise, or hedge.
Goal seek
Solve for an input value
Pick the input you want to vary and the output you care about. We'll find the input value that gets you to the target. Bisection-based; converges in < 50 iterations.
Monte Carlo simulation
Distribution under input uncertainty (500 trials)
We perturb every numeric input with normal-distributed noise (10–25% sigma depending on input type) and run 500 compute trials. The output is a probability distribution, not a single number — closer to how finance actually works.
Most-leveraged inputs (sensitivity analysis)
Where to focus — what moves the answer most
Each input perturbed ±10%; measured impact on Direct Roth eligibility (MAGI $285,000). Higher elasticity = bigger lever.
- 1
Modified AGI (MAGI)
Elasticity ↕ 0.00× — 10% change in this input affects Direct Roth eligibility (MAGI $285,000) by 0.0%.
- 2
Age (catch-up at 50+)
Elasticity ↕ 0.00× — 10% change in this input affects Direct Roth eligibility (MAGI $285,000) by 0.0%.
- 3
Existing Traditional IRA balance (pre-tax)
Elasticity ↕ 0.00× — 10% change in this input affects Direct Roth eligibility (MAGI $285,000) by 0.0%.
- 4
Current 401(k) employee deferral
Elasticity ↕ 0.00× — 10% change in this input affects Direct Roth eligibility (MAGI $285,000) by 0.0%.
ShowMath is the only calc site that surfaces this. Adjust the highest-leverage input first — that's where small moves create big results.
Chain payload (for the 3D constellation)
{
"slug": "backdoor-roth-master",
"depth": 1,
"primitives": [
"roth-ira-eligibility",
"backdoor-roth-calculator",
"mega-backdoor-roth-calculator",
"compound-interest-calculator"
],
"composes": [],
"chain": [
{
"key": "direct_roth",
"label": "Direct Roth eligibility (MAGI $285,000)",
"primitive": "roth-ira-eligibility",
"numeric": 0
},
{
"key": "backdoor_path",
"label": "Backdoor Roth path",
"primitive": "backdoor-roth-calculator",
"numeric": 2578.9473684210525
},
{
"key": "pro_rata_warning",
"label": "Pro-rata rule cost",
"numeric": 1414.7368421052631
},
{
"key": "mega_backdoor",
"label": "Mega-backdoor capacity (after-tax + rollover)",
"primitive": "mega-backdoor-roth-calculator",
"numeric": 0
},
{
"key": "total_annual_roth",
"label": "Total annual Roth capacity",
"numeric": 2578.9473684210525
},
{
"key": "thirty_year_growth",
"label": "30-year value (7% real)",
"primitive": "compound-interest-calculator",
"numeric": 243609.3963086015
},
{
"key": "tax_value",
"label": "Tax saved over 30 yrs (vs taxable)",
"numeric": 39565.352110920845
}
]
}The chain explained
Each step above corresponds to a primitive calculator. Click any to see the stand-alone version with its own explainer + sources.
- roth ira eligibilityshipping soon
- backdoor roth calculatorshipping soon
- mega backdoor roth calculatorshipping soon
- compound interest calculatorshipping soon
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